Warped product submanifolds of Kaehler manifolds with a slant factor

Bayram Sahin¹

¹Department of Mathematics Inonu University 44280, Malatya, Turkey

Annales Polonici Mathematici, Tome 95 (2009) no. 3, pp. 207-226

Résumé

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.

Détail

DOI : 10.4064/ap95-3-2

Keywords: recently showed there exist warped product semi slant submanifolds kaehler manifolds other carriazo introduced anti slant submanifolds particular class bi slant submanifolds paper study submanifolds detail useful define kind warped product submanifolds kaehler manifolds direction obtain existence warped product hemi slant anti slant submanifolds examples characterization theorem establish inequality squared norm second fundamental form terms warping function submanifolds equality considered