A characterization of totally umbilical hypersurfaces of a space form by geodesic mapping

E. Ö Canfes; A. Özdeǧer

doi:10.1007/s11253-013-0801-y

A characterization of totally umbilical hypersurfaces of a space form by geodesic mapping

E. Ö Canfes
, A. Özdeǧer

Department of Mathematics Engineering

Istanbul Technical University

Research output: Contribution to journal › Article › peer-review

Abstract

The idea of considering the second fundamental form of a hypersurface as the first fundamental form of another hypersurface has found very useful applications in Riemannian and semi-Riemannian geometry, especially when trying to characterize extrinsic hyperspheres and ovaloids. Recently, T. Adachi and S. Maeda gave a characterization of totally umbilical hypersurfaces in a space form by circles. In our paper, we give a characterization of totally umbilical hypersurfaces of a space form by means of geodesic mapping.

Original language	English
Pages (from-to)	643-648
Number of pages	6
Journal	Ukrainian Mathematical Journal
Volume	65
Issue number	4
DOIs	https://doi.org/10.1007/s11253-013-0801-y
Publication status	Published - Sept 2013

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AB - The idea of considering the second fundamental form of a hypersurface as the first fundamental form of another hypersurface has found very useful applications in Riemannian and semi-Riemannian geometry, especially when trying to characterize extrinsic hyperspheres and ovaloids. Recently, T. Adachi and S. Maeda gave a characterization of totally umbilical hypersurfaces in a space form by circles. In our paper, we give a characterization of totally umbilical hypersurfaces of a space form by means of geodesic mapping.

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A characterization of totally umbilical hypersurfaces of a space form by geodesic mapping

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