B. Y. Chen [Arch. Math. (Basel) 74 (2000), 154-160] proved a geometrical inequality for Lagrangian submanifolds in complex space forms in terms of the Ricci curvature and the squared mean curvature. Recently, this Chen-Ricci inequality was improved in [Int. Electron. J. Geom. 2 (2009), 39-45]. On the other hand, K. Arslan et al. [Int. J. Math. Math. Sci. 29 (2002), 719-726] established a Chen-Ricci inequality for submanifolds, in particular in contact slant submanifolds, in Kenmotsu space forms. In this article, we improve the latter inequality for special slant submanifolds in Kenmotsu space forms. We also investigate the equality case.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap110-1-7,
author = {Simona Costache and Iuliana Zamfir},
title = {An improved Chen-Ricci inequality for special slant submanifolds in Kenmotsu space forms},
journal = {Annales Polonici Mathematici},
volume = {111},
year = {2014},
pages = {81-89},
zbl = {1296.53112},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap110-1-7}
}
Simona Costache; Iuliana Zamfir. An improved Chen-Ricci inequality for special slant submanifolds in Kenmotsu space forms. Annales Polonici Mathematici, Tome 111 (2014) pp. 81-89. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap110-1-7/