On semiparallel and weyl-semiparallel hypersurfaces of kaehler manifolds

Özgür C., MURATHAN C., ARSLAN K.

Kyungpook Mathematical Journal, cilt.49, sa.1, ss.133-141, 2009 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 49 Sayı: 1
  • Basım Tarihi: 2009
  • Doi Numarası: 10.5666/kmj.2009.49.1.133
  • Dergi Adı: Kyungpook Mathematical Journal
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.133-141
  • Anahtar Kelimeler: Sasakian manifold, Kaehler manifold, Calabi-Yau manifold, semiparallel submanifold, Weyl-semiparallel submanifold, pseudoparallel submanifold
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

We study on semiparallel and Weyl semiparallel Sasakian hypersurfaces of Kaehler manifolds. We prove that a (2n + 1)-dimensional Sasakian hypersurface M of a (2n+2)-dimensional Kaehler manifold M2n+2 is semiparallel if and only if it is totally umbilical with unit mean curvature, if dimM = 3 and M4 is a Calabi-Yau manifold, then M is flat at each point of M. We also prove that such a hypersurface M is Weyl-semiparallel if and only if it is either an η-Einstein manifold or semiparallel. We also investigate the extended classes of semiparallel and Weyl semiparallel Sasakian hypersurfaces of Kaehler manifolds.