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

Canfes E., Ozdeger A.

UKRAINIAN MATHEMATICAL JOURNAL, cilt.65, sa.4, ss.643-648, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 65 Sayı: 4
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1007/s11253-013-0801-y
  • Dergi Adı: UKRAINIAN MATHEMATICAL JOURNAL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.643-648
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

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.