A characterization of totally umbilical hypersurfaces of a space form by geodesic mapping
Authors
E. Ö. Canfes
Istanbul Techn. Univ., Kadir Has Univ., Istanbul, Turkey
A. Özdeğer
Istanbul Techn. Univ., Kadir Has Univ., Istanbul, Turkey
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.
