Warped product submanifolds of Kaehler manifolds with a slant factor

Sahin B.

ANNALES POLONICI MATHEMATICI, vol.95, no.3, pp.207-226, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 95 Issue: 3
  • Publication Date: 2009
  • Doi Number: 10.4064/ap95-3-2
  • Journal Name: ANNALES POLONICI MATHEMATICI
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.207-226
  • Inonu University Affiliated: No

Abstract

Recently, we showed that there exist no warped product semi-slant submanifolds in Kaehler manifolds. On the other hand, Carriazo introduced anti-slant submanifolds as a particular class of bi-slant submanifolds. In this paper, we study such submanifolds in detail and show that they are useful to define a new kind of warped product submanifolds of Kaehler manifolds. In this direction, we obtain the existence of warped product hemi-slant (anti-slant) submanifolds with examples. We give a characterization theorem and establish an inequality for the squared norm of the second fundamental form in terms of the warping function for such submanifolds. The equality case is also considered.