2017
Том 69
№ 9

All Issues

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

Canfes E. Ö., Özdeğer A.

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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, specially 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 this paper, we give a characterization of totally umbilical hypersurfaces of a space form by means of geodesic mapping.

English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 4, pp 643-648.

Citation Example: Canfes E. Ö., Özdeğer A. A characterization of totally umbilical hypersurfaces of a space form by geodesic mapping // Ukr. Mat. Zh. - 2013. - 65, № 4. - pp. 583-587.

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