Kodai Mathematical Journal

Sectional curvatures of geodesic spheres in a complex hyperbolic space

Tetsuo Kajiwara and Sadahiro Maeda

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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.

Article information

Source
Kodai Math. J., Volume 38, Number 3 (2015), 604-619.

Dates
First available in Project Euclid: 30 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1446210597

Digital Object Identifier
doi:10.2996/kmj/1446210597

Mathematical Reviews number (MathSciNet)
MR3417524

Zentralblatt MATH identifier
06530869

Citation

Kajiwara, Tetsuo; Maeda, Sadahiro. Sectional curvatures of geodesic spheres in a complex hyperbolic space. Kodai Math. J. 38 (2015), no. 3, 604--619. doi:10.2996/kmj/1446210597. https://projecteuclid.org/euclid.kmj/1446210597


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