Open Access
October 2015 Sectional curvatures of geodesic spheres in a complex hyperbolic space
Tetsuo Kajiwara, Sadahiro Maeda
Kodai Math. J. 38(3): 604-619 (October 2015). DOI: 10.2996/kmj/1446210597

Abstract

We characterize geodesic spheres with sufficiently small radii in a complex hyperbolic space of constant holomorphic sectional curvature c(<0) by using their geometric three properties. These properties are based on their contact forms, geodesics and shape operators. These geodesic spheres are the only examples of hypersurfaces of type (A) which are of nonnegative sectional curvature in this ambient space. Moreover, in particular, when −1 ≤ c < 0, the class of these geodesic spheres has just one example of Sasakian space forms.

Citation

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Tetsuo Kajiwara. Sadahiro Maeda. "Sectional curvatures of geodesic spheres in a complex hyperbolic space." Kodai Math. J. 38 (3) 604 - 619, October 2015. https://doi.org/10.2996/kmj/1446210597

Information

Published: October 2015
First available in Project Euclid: 30 October 2015

MathSciNet: MR3417524
zbMATH: 06530869
Digital Object Identifier: 10.2996/kmj/1446210597

Rights: Copyright © 2015 Tokyo Institute of Technology, Department of Mathematics

Vol.38 • No. 3 • October 2015
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