A characterization of totally umbilical hypersurfaces of a space form by geodesic mapping
AbstractThe 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.
How to Cite
Canfes, E. Ö., and A. Özdeğer. “A Characterization of Totally Umbilical Hypersurfaces of a Space Form by Geodesic Mapping”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, no. 4, Apr. 2013, pp. 583-7, https://umj.imath.kiev.ua/index.php/umj/article/view/2441.