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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap95-3-2,
author = {Bayram Sahin},
title = {Warped product submanifolds of Kaehler manifolds with a slant factor},
journal = {Annales Polonici Mathematici},
volume = {95},
year = {2009},
pages = {207-226},
zbl = {1162.53040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap95-3-2}
}
Bayram Sahin. Warped product submanifolds of Kaehler manifolds with a slant factor. Annales Polonici Mathematici, Tome 95 (2009) pp. 207-226. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap95-3-2/