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 | |
| Publication status | Published - Sept 2013 |