Ricci Generalized Pseudo-Parallel Kaehlerian Submanifolds in Complex Space Forms

Yildiz A., MURATHAN C.

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, vol.31, no.2, pp.153-163, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 2
  • Publication Date: 2008
  • Journal Name: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.153-163
  • Keywords: Pseudosymmetry type manifolds, semisymmetric manifolds, hypersurfaces, pseudo-parallel, Ricci generalized pseudo-parallel, Kaehlerian submanifolds, HYPERSURFACES, CURVATURE
  • Bursa Uludag University Affiliated: Yes

Abstract

Let (M) over cap (m)(c) be a complex m-dimensional space form of holomorphic sectional curvature c and M-n be a complex n-dimensional Kaehlerian submanifold of (M) over cap (m) (c). We prove that if M-n is Ricci generalized pseudo-parallel,, then either M-n is totally geodesic, or parallel to h parallel to(2) = -2/3 (LT - 1/2 (n + 2)c), or at some point x of M-n, parallel to h parallel to(2) (x) > -2/3 (L(x)T(x) - 1/2 (n + 2)c).