Patrick J. Ryan

Generating author description...

All published works

Action	Title	Year	Authors
+	On the Work of Cartan and Münzner on Isoparametric Hypersurfaces	2025	Thomas E. Cecil Patrick J. Ryan
+ PDF Chat	SZEMERÉDI’S THEOREM: AN EXPLORATION OF IMPURITY, EXPLANATION, AND CONTENT	2021	Patrick J. Ryan
+	Hypersurfaces with Codazzi-type shape operator for a Tanaka--Webster connection	2015	Thomas Ivey Patrick J. Ryan
+ PDF Chat	HYPERSURFACES IN P<sup>2</sup> AND H<sup>2</sup> WITH TWO DISTINCT PRINCIPAL CURVATURES	2015	Thomas Ivey Patrick J. Ryan
+	Gaps between zeros of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="normal">GL</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> L-functions	2015	Owen Barrett Brian McDonald Steven J. Miller Patrick J. Ryan Caroline L. Turnage‐Butterbaugh Karl Winsor
+	Real Hypersurfaces in Complex Space Forms	2015	Thomas E. Cecil Patrick J. Ryan
+	Submanifolds in Lie Sphere Geometry	2015	Thomas E. Cecil Patrick J. Ryan
+	Complex Submanifolds of CP n and CH n	2015	Thomas E. Cecil Patrick J. Ryan
+	Geometry of Hypersurfaces	2015	Thomas E. Cecil Patrick J. Ryan
+	Hypersurfaces in Quaternionic Space Forms	2015	Thomas E. Cecil Patrick J. Ryan
+	Submanifolds of Real Space Forms	2015	Thomas E. Cecil Patrick J. Ryan
+	Hopf Hypersurfaces	2015	Thomas E. Cecil Patrick J. Ryan
+	Dupin Hypersurfaces	2015	Thomas E. Cecil Patrick J. Ryan
+ PDF Chat	Isoparametric Hypersurfaces	2015	Thomas E. Cecil Patrick J. Ryan
+	Introduction	2015	Thomas E. Cecil Patrick J. Ryan
+	Indeterminate Strings, Prefix Arrays & Undirected Graphs	2014	Manolis Christodoulakis Patrick J. Ryan W.F. Smyth Shu Wang
+	Large gaps between zeros ofGL(2)L-functions	2014	Owen Barrett Brian McDonald Patrick J. Ryan Karl Winsor Steven J. Miller
+	Hypersurfaces in $CP^2$ and $CH^2$ with two distinct principal curvatures	2013	Thomas Ivey Patrick J. Ryan
+	Hypersurfaces in $CP^2$ and $CH^2$ with two distinct principal curvatures	2013	Thomas Ivey Patrick J. Ryan
+ PDF Chat	The $^{*}$-Ricci Tensor for Hypersurfaces in $\mathbb{C}\mathbb{P}^n$ and $\mathbb{C}\mathrm{H}^n$	2011	Thomas Ivey Patrick J. Ryan
+	The *-Ricci tensor for hypersurfaces in CP^n and CH^n	2010	Thomas Ivey Patrick J. Ryan
+	The Structure Jacobi Operator for Real Hypersurfaces in $${{\mathbb{C}} {\mathbb{P}}^2}$$ and $${\mathbb {C}{\rm H}^2}$$	2009	Thomas Ivey Patrick J. Ryan
+	Hopf hypersurfaces of small Hopf principal curvature in $${\mathbb{C}{\rm H}^2}$$	2008	Thomas Ivey Patrick J. Ryan
+	A classification of pseudo-Einstein hypersurfaces in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="bold">C</mml:mi><mml:msup><mml:mi>P</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math>	2008	Hyang Sook Kim Patrick J. Ryan
+	The structure Jacobi operator for hypersurfaces in CP^2 and CH^2	2008	Thomas Ivey Patrick J. Ryan
+	Hopf Hypersurfaces of Small Hopf Principal Curvature in CH^2	2008	Thomas Ivey Patrick J. Ryan
+	Semi-parallel and Semi-symmetric Real Hypersurfaces in Complex Space Forms	1998	Ross Niebergall Patrick J. Ryan
+ PDF Chat	Affine Dupin Surfaces	1996	Ross Niebergall Patrick J. Ryan
+	Affine isoparametric hypersurfaces	1994	Ross Niebergall Patrick J. Ryan
+ PDF Chat	Affine 3-Spheres with Constant Affine Curvature	1992	Martin A. Magid Patrick J. Ryan
+ PDF Chat	Affine 3-spheres with constant affine curvature	1992	Martin A. Magid Patrick J. Ryan
+	The projective plane <b>P</b><sup>2</sup>	1986	Patrick J. Ryan
+	Proof of Theorem 2.2	1986	Patrick J. Ryan
+	Euclidean and Non-Euclidean Geometry: An Analytic Approach	1986	Patrick J. Ryan
+	Plane Euclidean geometry	1986	Patrick J. Ryan
+	Distance geometry on <b>P</b><sup>2</sup>	1986	Patrick J. Ryan
+	Affine transformations in the Euclidean plane	1986	Patrick J. Ryan
+	Finite groups of isometries of <b>E</b><sup>2</sup>	1986	Patrick J. Ryan
+	The hyperbolic plane	1986	Patrick J. Ryan
+	Geometry on the sphere	1986	Patrick J. Ryan
+	Trigonometric and hyperbolic functions	1986	Patrick J. Ryan
+	Euclidean and Non-Euclidean Geometry	1986	Patrick J. Ryan
+	The Principal Curvatures of the Monkey Saddle	1986	Thomas E. Cecil Patrick J. Ryan
+	On the Number of Top-Cycles of a Tight Surface in 3-Space	1984	Thomas E. Cecil Patrick J. Ryan
+ PDF Chat	Focal sets and real hypersurfaces in complex projective space	1982	Thomas E. Cecil Patrick J. Ryan
+	Focal Sets and Real Hypersurfaces in Complexes Projective Space	1982	Thomas E. Cecil Patrick J. Ryan
+	Tight spherical embeddings	1981	Thomas E. Cecil Patrick J. Ryan
+ PDF Chat	Conformal Geometry and the Cyclides of Dupin	1980	Thomas E. Cecil Patrick J. Ryan
+ PDF Chat	Distance functions and umbilic submanifolds of hyperbolic space	1979	Thomas E. Cecil Patrick J. Ryan
+ PDF Chat	Focal sets of submanifolds	1978	Thomas E. Cecil Patrick J. Ryan
+	Kähler manifolds as real hypersurfaces	1973	Patrick J. Ryan
+ PDF Chat	A class of complex hypersurfaces	1972	Patrick J. Ryan
+	Hypersurfaces with parallel Ricci tensor	1971	Patrick J. Ryan
+ PDF Chat	Homogeneity and some curvature conditions for hypersurfaces	1969	Patrick J. Ryan

Common Coauthors

Coauthor	Papers Together
Thomas E. Cecil	19
Thomas Ivey	10
Ross Niebergall	3
Owen Barrett	2
Brian McDonald	2
Karl Winsor	2
Martin A. Magid	2
Steven J. Miller	2
W.F. Smyth	1
Caroline L. Turnage‐Butterbaugh	1
Hyang Sook Kim	1
Shu Wang	1
Manolis Christodoulakis	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Real hypersurfaces of a complex hyperbolic space	1985	Sebastián Montiel	11
+ PDF Chat	Real hypersurfaces in a complex projective space with constant principal curvatures	1975	Ryoichi Takagi	9
+	Foundations of Differential Geometry	1963	Shôshichi Kobayashi Katsumi Nomizu	7
+	The quadratic slice theorem and the equiaffine tube theorem for equiaffine Dupin hypersurfaces	2005	Naoyuki Koike	7
+ PDF Chat	Pseudo-Einstein real hypersurfaces in complex space forms	1979	Masahiro Kon	7
+	Real Hypersurfaces in Complex Space Forms	2015	Thomas E. Cecil Patrick J. Ryan	6
+ PDF Chat	On real hypersurfaces of a complex projective space	1976	Yoshiaki Maeda	6
+	A classification of pseudo-Einstein hypersurfaces in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="bold">C</mml:mi><mml:msup><mml:mi>P</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math>	2008	Hyang Sook Kim Patrick J. Ryan	6
+ PDF Chat	Homogeneity and some curvature conditions for hypersurfaces	1969	Patrick J. Ryan	6
+ PDF Chat	Real hypersurfaces and complex submanifolds in complex projective space	1986	Makoto Kimura	6
+ PDF Chat	Focal sets and real hypersurfaces in complex projective space	1982	Thomas E. Cecil Patrick J. Ryan	6
+	On homogeneous real hypersurfaces in a complex projective space	1973	Ryoichi Takagi	6
+ PDF Chat	A characterization of metric spheres in hyperbolic space by Morse theory	1974	Thomas E. Cecil	5
+ PDF Chat	Deformations of Dupin hypersurfaces	1989	Ulrich Pinkall Gudlaugur Thorbergsson	5
+ PDF Chat	Real hypersurfaces with constant principal curvatures in complex hyperbolic space.	1989	Jürgen Berndt	5
+ PDF Chat	Cartan for Beginners	2003	Thomas Ivey J. M. Landsberg	5
+	Isoparametrische Hyperflächen in Sphären	1980	Hans Münzner	5
+	Hopf hypersurfaces in space forms	2004	José Kenedy Martins	4
+	Fundamentals of linear algebra	1966	Katsumi Nomizu	4
+ PDF Chat	On some types of isoparametric hypersurfaces in spheres, II	1976	Hideki Ozeki Masaru Takeuchi	4
+ PDF Chat	Focal sets of submanifolds	1978	Thomas E. Cecil Patrick J. Ryan	4
+ PDF Chat	Real hypersurfaces in a complex projective space with constant principal curvatures II	1975	Ryoichi Takagi	4
+	On the eigenvalues of the shape operator of an isometric immersion into a space of constant curvature	1979	Helmut Reckziegel	4
+	Cliffordalgebren und neue isoparametrische Hyperfl�chen	1981	Dirk Ferus Hermann Karcher Hans-Friedrich M�nzner	4
+	Hypersurfaces with parallel Ricci tensor	1971	Patrick J. Ryan	4
+	Dupin Hypersurfaces	1983	Gudlaugur Thorbergsson	4
+	Sectional curvatures of holomorphic planes on a real hypersurface inP n (C)	1987	Makoto Kimura	4
+	Élie Cartan’s work on isoparametric families of hypersurfaces	1975	Katsumi Nomizu	4
+	Familles de surfaces isoparamétriques dans les espaces à courbure constante	1938	Élie Cartan	4
+	Sur des familles remarquables d'hypersurfaces isoparamétriques dans les espaces sphériques	1939	Élie Cartan	4
+ PDF Chat	A variational problem for surfaces in Laguerre geometry	1996	Emilio Musso Lorenzo Nicolodi	4
+	Applications of the Theory of Morse to Symmetric Spaces	1958	Raoul Bott Hans Samelson	4
+	Exterior Differential Systems	1991	Robert L. Bryant Shiing-Shen Chern Robert B. Gardner Hubert Goldschmidt P. A. Griffiths	4
+	Tight immersions of highly connected manifolds	1986	Gudlaugur Thorbergsson	4
+ PDF Chat	Isoparametric and Dupin Hypersurfaces	2008	Thomas E. Cecil	3
+ PDF Chat	Minimal imbeddings of $R$-spaces	1968	Masaru Takeuchi Shôshichi Kobayashi	3
+ PDF Chat	Real hypersurfaces with constant principal curvatures in the complex hyperbolic plane	2007	Jürgen Berndt José Carlos Díaz-Ramos	3
+	Tight and Taut Submanifolds	2011	Thomas E. Cecil Shiing-Shen Chern	3
+ PDF Chat	Taut immersions of noncompact surfaces into a Euclidean 3-space	1976	Thomas E. Cecil	3
+	Flat affine spheres in R 3	1990	M. Magid PatrickJ. Ryan	3
+ PDF Chat	Geometric applications of critical point theory to submanifolds of complex projective space	1974	Thomas E. Cecil	3
+	The Structure Jacobi Operator for Real Hypersurfaces in $${{\mathbb{C}} {\mathbb{P}}^2}$$ and $${\mathbb {C}{\rm H}^2}$$	2009	Thomas Ivey Patrick J. Ryan	3
+	A global formulation of the Lie theory of transformation groups	1957	Richard S. Palais	3
+	Dupin hypersurfaces with four principal curvatures in ℝ5 with principal coordinates	2009	Carlos M. C. Riveros	3
+ PDF Chat	On Fubinian and $C$-Fubinian manifolds	1963	Yoshihiro Tashiro Shun-ichi Tachibana	3
+	Characteristic roots and vectors of a diifferentiable family of symmetric matrices<sup>†</sup>	1973	Katsumi Nomizu	3
+ PDF Chat	Real hypersurfaces in quaternionic projective space	1986	Antonio Martínez Juan de Dios Pérez	3
+ PDF Chat	Smoothness theorems for the principal curvatures and principal vectors of a hypersurface	1975	Donald H. Singley	3
+ PDF Chat	A class of hypersurfaces with constant principal curvatures in a sphere	1976	Ryoichi Takagi	3
+	Isoparametric functions on Riemannian manifolds. I	1987	Wang Qiming	3