Length spectrum of geodesic spheres in a non-flat complex space form

Toshiaki Adachi, Sadahiro Maeda, Masakazu Yamagishi

Type: Article

Publication Date: 2002-04-01

Citations: 26

DOI: https://doi.org/10.2969/jmsj/05420373

Abstract

We investigate the distribution of length of closed geodesics on geodesic spheres and tubes around complex hyperplane in a non-flat complex space form. The feature of the length spectrum of a geodesic sphere of radius r in a complex projective space of holomorphic sectional curvature 4 is quite different according as tan2r is rational or irrational. Each length spectrum is simple when tan2r is irrationaj but when tan2r is rationaj it is not necessarily simple and moreover the multiplicity is not uniformly bounded.

Locations

Journal of the Mathematical Society of Japan - View - PDF

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Works Cited by This (19)

Action	Title	Year	Authors
+	Differential geometry of geodesic spheres.	1981	Lieven Vanhecke Bing‐Yu Chen
+	Circles in a complex projective space	1995	Toshiaki Adachi Sadahiro Maeda Seiichi Udagawa
+ PDF Chat	Holomorphic helices in a complex space form	1997	Sadahiro Maeda Toshiaki Adachi
+	A Classical Introduction to Modern Number Theory	1982	Kenneth Ireland Michael Rosen
+ PDF Chat	Real hypersurfaces with constant principal curvatures in complex hyperbolic space.	1989	Jürgen Berndt
+	On homogeneous real hypersurfaces in a complex projective space	1973	Ryoichi Takagi
+ PDF Chat	Focal sets and real hypersurfaces in complex projective space	1982	Thomas E. Cecil Patrick J. Ryan
+ PDF Chat	Real hypersurfaces of a complex hyperbolic space	1985	Sebastián Montiel
+	Characterizations of geodesic hyperspheres in a complex projective space by observing the extrinsic shape of geodesics	1997	Sadahiro Maeda Koichi Ogiue
+	Helical geodesic immersions into complex space forms	1989	Sadahiro Maeda Yoshihiro Ohnita