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


Canfes E. , Ozdeger A.

UKRAINIAN MATHEMATICAL JOURNAL, vol.65, no.4, pp.643-648, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 65 Issue: 4
  • Publication Date: 2013
  • Doi Number: 10.1007/s11253-013-0801-y
  • Title of Journal : UKRAINIAN MATHEMATICAL JOURNAL
  • Page Numbers: pp.643-648

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.