Masatomo Takahashi

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All published works

Action	Title	Year	Authors
+ PDF Chat	Bertrand lightcone framed curves in the Lorentz-Minkowski 3-space	2024	Nozomi Nakatsuyama Masatomo Takahashi
+ PDF Chat	Singularities of helicoidal surfaces of frontals in the Euclidean space	2024	Nozomi Nakatsuyama Kentaro Saji R. Shimada Masatomo Takahashi
+	Pseudo-circular evolutes and involutes of lightcone framed curves in the Lorentz-Minkowski 3-space	2024	Donghe Pei Masatomo Takahashi Wei Zhang
+	On Vertices of Frontals in the Euclidean Plane	2024	Nozomi Nakatsuyama Masatomo Takahashi
+ PDF Chat	Bertrand types of regular curves and Bertrand framed curves in the Euclidean 3-space	2024	Nozomi Nakatsuyama Masatomo Takahashi
+ PDF Chat	Lightcone framed curves in the Lorentz-Minkowski 3-space	2024	Liang Chen Masatomo Takahashi
+	Duality and geometry of horocyclic evolutes in hyperbolic plane	2024	Liang Chen Shyūichi Izumiya Masatomo Takahashi
+ PDF Chat	On vertices of frontals in the Euclidean plane	2024	Nozomi Nakatsuyama Masatomo Takahashi
+	On generalised framed surfaces in the Euclidean space	2024	Masatomo Takahashi Haiou Yu
+ PDF Chat	Mixed type of curves in the Lorentz-Minkowski space	2023	Liang Chen Masatomo Takahashi
+ PDF Chat	Bertrand and Mannheim curves of framed curves in the 4-dimensional Euclidean space	2023	Shun’ichi Honda Masatomo Takahashi Haiou Yu
+ PDF Chat	One‐parameter families of Legendre curves and plane line congruences	2022	Yutaro Kabata Masatomo Takahashi
+	Enveloids of Legendre Curves in the Unit Tangent Bundle over the Euclidean Plane	2022	Enze Li Donghe Pei Masatomo Takahashi
+ PDF Chat	Bertrand and Mannheim Curves of Spherical Framed Curves in a Three-Dimensional Sphere	2022	Masatomo Takahashi Haiou Yu
+	Singularities of Translation Surfaces in the Euclidean 3-Space	2022	Tomonori Fukunaga Masatomo Takahashi
+	Equi-affine plane curves with singular points	2022	Masatomo Takahashi
+	Bertrand and Mannheim curves of framed curves in the 4-dimensional Euclidean space	2022	Shun’ichi Honda Masatomo Takahashi
+	Circular evolutes and involutes of framed curves in the Euclidean space	2021	Shun’ichi Honda Masatomo Takahashi
+	Envelopes of families of framed surfaces and singular solutions of first-order partial differential equations	2020	Masatomo Takahashi Haiou Yu
+	Singularities of Singular Solutions of First-Order Differential Equations of Clairaut Type	2020	Kentaro Saji Masatomo Takahashi
+	Bertrand and Mannheim curves of framed curves in the3-dimensional Euclidean space	2020	Shun’ichi Honda Masatomo Takahashi
+	Dualities and envelopes of one‐parameter families of frontals in hyperbolic and de Sitter 2‐spaces	2020	Liang Chen Donghe Pei Masatomo Takahashi
+	On families of Lagrangian submanifolds	2020	Shyūichi Izumiya Masatomo Takahashi
+	Horo-flat surfaces along cuspidal edges in the hyperbolic space	2020	Shyūichi Izumiya Maria Carmen Romero-Fuster Kentaro Saji Masatomo Takahashi
+ PDF Chat	Surfaces of Revolution of Frontals in the Euclidean Space	2019	Masatomo Takahashi Keisuke Teramoto
+ PDF Chat	Envelopes of one-parameter families of framed curves in the Euclidean space	2019	Donghe Pei Masatomo Takahashi Haiou Yu
+	Developable surfaces along frontal curves on embedded surfaces	2019	Shun’ichi Honda Shyūichi Izumiya Masatomo Takahashi
+ PDF Chat	Evolutes and focal surfaces of framed immersions in the Euclidean space	2019	Shun’ichi Honda Masatomo Takahashi
+	Geometric equivalence among smooth map germs	2019	Shyūichi Izumiya Masatomo Takahashi Hiroshi Teramoto
+	Envelopes of families of Legendre mappings in the unit tangent bundle over the Euclidean space	2018	Masatomo Takahashi
+ PDF Chat	Evolutes of curves in the Lorentz-Minkowski plane	2018	S. Izumiya M. C. Romero Fuster Masatomo Takahashi
+ PDF Chat	Framed Surfaces in the Euclidean Space	2018	Tomonori Fukunaga Masatomo Takahashi
+ PDF Chat	Geometric equivalence among smooth map germs	2018	Shyūichi Izumiya Masatomo Takahashi Hiroshi Teramoto
+ PDF Chat	Envelopes of legendre curves in the unit spherical bundle over the unit sphere	2017	Yanlin Li Donghe Pei Masatomo Takahashi Haiou Yu
+	Framed surfaces in the Euclidean space	2017	Tomonori Fukunaga Masatomo Takahashi
+ PDF Chat	Existence conditions of framed curves for smooth curves	2017	Tomonori Fukunaga Masatomo Takahashi
+ PDF Chat	Envelopes of Legendre Curves in the Unit Tangent Bundle over the Euclidean Plane	2016	Masatomo Takahashi
+ PDF Chat	Framed curves in the Euclidean space	2016	Shun’ichi Honda Masatomo Takahashi
+ PDF Chat	On convexity of simple closed frontals	2016	Tomonori Fukunaga Masatomo Takahashi
+	Envelopes of Legendre curves in the unit tangent bundle over the Euclidean plane	2016	Masatomo Takahashi
+	Existence conditions of framed curves for smooth curves	2016	Tomonori Fukunaga Masatomo Takahashi
+ PDF Chat	Singularities of tangent surfaces in Cartan’s split $G_2$-geometry	2016	Goo Ishikawa Yoshinori Machida Masatomo Takahashi
+ PDF Chat	Legendre curves in the unit spherical bundle over the unit sphere and evolutes	2016	Masatomo Takahashi
+	Dualities and evolutes of fronts in hyperbolic and de Sitter space	2015	Liang Chen Masatomo Takahashi
+ PDF Chat	Involutes of fronts in the Euclidean plane	2015	Tomonori Fukunaga Masatomo Takahashi
+	Legendre curves in the unit spherical bundle and evolutes	2015	Masatomo Takahashi
+	Dualities and evolutes of fronts in hyperbolic 2-space and de Sitter 2-space	2015	Liang Chen Masatomo Takahashi
+	On convexity of simple closed frontals	2015	Tomonori Fukunaga Masatomo Takahashi
+ PDF Chat	Evolutes and Involutes of Frontals in the Euclidean Plane	2015	Tomonori Fukunaga Masatomo Takahashi
+ PDF Chat	Geometry of D_4 conformal triality and singularities of tangent surfaces	2015	Goo Ishikawa Yoshinori Machida Masatomo Takahashi
+	D_n-geometry and singularities of tangent surfaces	2014	Goo Ishikawa Yoshinori Machida Masatomo Takahashi
+	Evolutes and involutes of frontals in the Euclidean plane	2014	Tomonori Fukunaga Masatomo Takahashi
+	Geometry of D_4 conformal triality and singularities of tangent surfaces	2014	Goo Ishikawa Yoshinori Machida Masatomo Takahashi
+	Classifications of completely integrable implicit second order ordinary differential equations	2014	Masatomo Takahashi
+ PDF Chat	Evolutes of fronts in the Euclidean plane	2014	T. Fukunga Masatomo Takahashi
+	Involutes of fronts in the Euclidean plane	2013	Tomonori Fukunaga Masatomo Takahashi
+ PDF Chat	Existence and uniqueness for Legendre curves	2013	Tomonori Fukunaga Masatomo Takahashi
+	Evolutes of fronts in the Euclidean plane	2012	Tomonori Fukunaga Masatomo Takahashi
+	Singularities of tangent surfaces in Cartan's split G2-geometry	2012	Goo Ishikawa Yoshinori Machida Masatomo Takahashi
+	PEDAL FOLIATIONS AND GAUSS MAPS OF HYPERSURFACES IN EUCLIDEAN SPACE	2012	Shyūichi Izumiya Masatomo Takahashi
+ PDF Chat	Pedal foliations and Gauss maps of hypersurfaces in Euclidean space	2012	Shyūichi Izumiya Masatomo Takahashi
+	Completely integrable inplicit ordinary differential equations	2012	Masatomo Takahashi
+	On caustics of submanifolds and canal hypersurfaces in Euclidean space	2011	Shyūichi Izumiya Masatomo Takahashi
+	The asymmetry on singularities of tangent surfaces in contact-cone Legendre-null duality	2011	Goo Ishikawa Yoshinori Machida Masatomo Takahashi
+	Folding maps on spacelike and timelike surfaces and duality	2010	Shyūichi Izumiya Masatomo Takahashi Farid Tari
+	Caustics and wave front propagations (Singularity theory of smooth maps and related geometry)	2010	Masatomo Takahashi
+	On completely integrable implicit ordinary differential equations	2010	Masatomo Takahashi
+ PDF Chat	Horospherical flat surfaces in Hyperbolic 3-space	2010	Shyūichi Izumiya Kentaro Saji Masatomo Takahashi
+	A sufficient condition that contact equivalence implies right equivalence for smooth function germs	2009	Masatomo Takahashi
+	Classifications of implicit second-order ordinary differential equations of Clairaut type	2008	Yoshinori Machida Masatomo Takahashi
+	Caustics and wave front propagations: applications to differential geometry	2008	Shyūichi Izumiya Masatomo Takahashi
+ PDF Chat	Bifurcations of completely integrable first-order ordinary differential equations	2007	Masatomo Takahashi
+	Folding maps on spacelike and timelike surfaces and duality	2007	Shyūichi Izumiya Masatomo Takahashi Farid Tari
+ PDF Chat	On Implicit Second-Order Ordinary Differential Equations: Completely Integrable and Clairaut Type	2007	Masatomo Takahashi
+	Horospherical flat surfaces in Hyperbolic 3-space	2007	Shyūichi Izumiya Kentaro Saji Masatomo Takahashi
+	Uniqueness for geometric solutions of implicit second order ordinary differential equations	2007	Masatomo Takahashi
+ PDF Chat	Spacelike parallels and evolutes in Minkowski pseudo-spheres	2007	Shyūichi Izumiya Masatomo Takahashi
+ PDF Chat	Singularities of smooth mappings with patterns	2007	Kentaro Saji Masatomo Takahashi
+ PDF Chat	On complete solutions and complete singular solutions of second order ordinary differential equations	2007	Masatomo Takahashi
+	On completely integrable first order ordinary differential equations	2007	Masatomo Takahashi
+ PDF Chat	Bifurcations of holonomic systems of general Clairaut type	2006	Masatomo Takahashi
+ PDF Chat	GLOBAL PROPERTIES OF SPACELIKE CURVES IN MINKOWSKI 3-SPACE	2006	Shyūichi Izumiya Makoto Kikuchi Masatomo Takahashi
+	Spacelike Parallels and Evolutes in Minkowski pseudo-spheres	2006	Shyūichi Izumiya Masatomo Takahashi
+	Singularities of smooth mappings with patterns	2005	Kentaro Saji Masatomo Takahashi
+	THE HOROSPHERICAL GEOMETRY OF SUBMANIFOLDS IN HYPERBOLIC SPACE	2005	S. Izumiya Donghe Pei M. C. Romero Fuster Masatomo Takahashi
+ PDF Chat	Holonomic systems of general Clairaut type	2005	Masatomo Takahashi
+	Global properties of spacelike curves in Minkowski 3-space	2005	Shyūichi Izumiya Makoto Kikuchi Masatomo Takahashi
+	Holonomic systems of general Clairaut type	2004	Masatomo Takahashi
+	On the horospherical ridges of submanifolds of codimension 2 in Hyperbolic n-space	2004	S. Izumiya Donghe Pei M. C. Romero-Fuster Masatomo Takahashi
+	The horospherical geomoetry of submanifolds in hyperbolic space	2004	Shyūichi Izumiya Donghe Pei M. C. Romero Fuster Masatomo Takahashi
+ PDF Chat	SINGULARITIES OF EVOLUTES OF HYPERSURFACES IN HYPERBOLIC SPACE	2004	Shyūichi Izumiya Donghe Pei Masatomo Takahashi
+	Curves and surfaces in hyperbolic space	2004	Shyūichi Izumiya Donghe Pei Masatomo Takahashi
+ PDF Chat	Bifurcations of ordinary differential equations of Clairaut type	2003	Masatomo Takahashi
+	Evolutes of hypersurfaces in Hyperbolic space	2002	S. Izumiya Donghe Pei Masatomo Takahashi
+	Bifurcations of ordinary differential equations of Clairaut type	2002	Masatomo Takahashi
+	An analogue of minimal surface theory in 𝑆𝐿(𝑛,𝐂)/𝐒𝐔(𝐧)	2001	Masatoshi Kokubu Masatomo Takahashi Masaaki Umehara Koji Yamada

Common Coauthors

Coauthor	Papers Together
Shyūichi Izumiya	21
Donghe Pei	11
Tomonori Fukunaga	11
Shun’ichi Honda	7
Yoshinori Machida	7
Kentaro Saji	7
Goo Ishikawa	6
Haiou Yu	6
Nozomi Nakatsuyama	5
S. Izumiya	4
M. C. Romero Fuster	3
Hiroshi Teramoto	2
Makoto Kikuchi	2
Liang Chen	2
Liang Chen	2
Farid Tari	2
Tomonori Fukunaga	2
Keisuke Teramoto	1
Yanlin Li	1
Enze Li	1
Wei Zhang	1
Liang Chen	1
Masaaki Umehara	1
R. Shimada	1
Yutaro Kabata	1
M. C. Romero-Fuster	1
Koji Yamada	1
T. Fukunga	1
Maria Carmen Romero-Fuster	1
Liang Chen	1
Masatoshi Kokubu	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Singularities of Differentiable Maps	1985	Vladimir I. Arnold S. M. Guseĭn-Zade Alexander Varchenko	27
+ PDF Chat	Existence and uniqueness for Legendre curves	2013	Tomonori Fukunaga Masatomo Takahashi	24
+	Curves and Singularities	1992	J. W. Bruce P. J. Giblin	20
+ PDF Chat	Reconstructions of fronts and caustics depending on a parameter and versality of mappings	1984	V. M. Zakalyukin	18
+	Modern Differential Geometry of Curves and Surfaces with Mathematica	2006	Alfred Gray	17
+ PDF Chat	Evolutes of fronts in the Euclidean plane	2014	T. Fukunga Masatomo Takahashi	16
+ PDF Chat	Framed curves in the Euclidean space	2016	Shun’ichi Honda Masatomo Takahashi	15
+	Elementary Geometry of Differentiable Curves: An Undergraduate Introduction	2001	C. G. Gibson	14
+ PDF Chat	Evolutes and Involutes of Frontals in the Euclidean Plane	2015	Tomonori Fukunaga Masatomo Takahashi	13
+	Singularities of smooth functions and maps	1982	Jean Martinet	12
+ PDF Chat	Spacelike parallels and evolutes in Minkowski pseudo-spheres	2007	Shyūichi Izumiya Masatomo Takahashi	11
+	Evolutes of Hyperbolic Plane Curves	2004	Shyūichi Izumiya Dong He Pei Takashi Sano Erika Torii	10
+	Elementary Geometry of Differentiable Curves	2001	C. G. Gibson	10
+	Singularities of flat fronts in hyperbolic space	2005	Masatoshi Kokubu Wayne Rossman Kentaro Saji Masaaki Umehara Kotaro Yamada	10
+ PDF Chat	Envelopes of Legendre Curves in the Unit Tangent Bundle over the Euclidean Plane	2016	Masatomo Takahashi	9
+ PDF Chat	SINGULARITIES OF HYPERBOLIC GAUSS MAPS	2003	Shyūichi Izumiya Donghe Pei Takasi Sano	9
+	Holonomic systems of Clairaut type	1995	Shyūichi Izumiya Yasuhiro Kurokawa	9
+	There is More than One Way to Frame a Curve	1975	Richard L. Bishop	9
+	Caustics and wave front propagations: applications to differential geometry	2008	Shyūichi Izumiya Masatomo Takahashi	9
+ PDF Chat	SINGULARITIES OF EVOLUTES OF HYPERSURFACES IN HYPERBOLIC SPACE	2004	Shyūichi Izumiya Donghe Pei Masatomo Takahashi	8
+	Simple Singularities of Mappings C, 0 → C<sup>2</sup> , 0	1982	J. W. Bruce Terence Gaffney	8
+	The Unfolding and Determinacy Theorems for Subgroups of A and K	1984	James Damon	8
+ PDF Chat	Framed Surfaces in the Euclidean Space	2018	Tomonori Fukunaga Masatomo Takahashi	8
+ PDF Chat	Singularities of maximal surfaces	2007	Shoichi Fujimori Kentaro Saji Masaaki Umehara Kotaro Yamada	7
+ PDF Chat	Legendrian Dualities and Spacelike Hypersurfaces in the Lightcone	2009	Sh. Izumiya	7
+ PDF Chat	Completely integrable holonomic systems of first-order differential equations	1995	Shyūichi Izumiya	6
+	Zariski’s moduli problem for plane branches and the classification of Legendre curve singularities	2007	Goo Ishikawa	6
+ PDF Chat	Book Review: Singularities of differentiable maps, Vol. 1. The classification of critical sets, caustics and wave fronts	1987	C. T. C. Wall	6
+ PDF Chat	Time-like hypersurfaces in de Sitter space and Legendrian singularities	2007	Shyūichi Izumiya	6
+	Curves and Singularities: A Geometrical Introduction to Singularity Theory.	1987	J. Callahan J. W. Bruce P. J. Giblin	6
+ PDF Chat	Singular Solutions of First-Order Differential Equations	1994	S. Izumiya	6
+ PDF Chat	The horospherical geometry of surfaces in hyperbolic 4-space	2006	Shyūichi Izumiya Donghe Pei María del Carmen Romero Fuster	5
+	On Generic Composites of Maps	1991	James Montaldi	5
+ PDF Chat	Involutes of fronts in the Euclidean plane	2015	Tomonori Fukunaga Masatomo Takahashi	5
+ PDF Chat	The geometry of fronts	2009	Kentaro Saji Masaaki Umehara Kotaro Yamada	5
+	CLASSIFICATION OF GENERIC INTEGRAL DIAGRAMS AND FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS	1994	Atsushi Hayakawa Goo Ishikawa S. Izumiya K. Yamaguchi	5
+	On the horospherical ridges of submanifolds of codimension 2 in Hyperbolic n-space	2004	S. Izumiya Donghe Pei M. C. Romero-Fuster Masatomo Takahashi	5
+	Evolutes and Involutes of Spatial Curves	2013	Dmitry Fuchs	5
+	On Clairaut-type equations	1994	Shyūichi Izumiya	5
+ PDF Chat	Geometric Invariants of Cuspidal Edges	2015	Luciana F. Martins Kentaro Saji	5
+	Symplectic Bifurcations of Plane Curves and Isotropic Liftings	2003	Goo Ishikawa	5
+ PDF Chat	Legendre curves in the unit spherical bundle over the unit sphere and evolutes	2016	Masatomo Takahashi	5
+	Curves in the Minkowski plane and their contact with pseudo-circles	2011	Amani Saloom Farid Tari	5
+	The theory of Legendrian unfoldings and first-order differential equations	1993	Shyūichi Izumiya	4
+ PDF Chat	Stability of Gauss maps	1978	David Bleecker L. Wilson	4
+ PDF Chat	Distance functions and umbilic submanifolds of hyperbolic space	1979	Thomas E. Cecil Patrick J. Ryan	4
+	THE HOROSPHERICAL GEOMETRY OF SUBMANIFOLDS IN HYPERBOLIC SPACE	2005	S. Izumiya Donghe Pei M. C. Romero Fuster Masatomo Takahashi	4
+	The Singularities of a Smooth n-Manifold in (2n - 1)-Space	1944	Hassler Whitney	4
+	Differential Geometry, Lie Groups, and Symmetric Spaces	2001	Sigurđur Helgason	4
+	On the Classification of Germs of Maps from R<sup>2</sup> to R<sup>3</sup>	1985	David Mond	4