Table of Contents
ISRN Geometry
Volume 2011 (2011), Article ID 374584, 12 pages
http://dx.doi.org/10.5402/2011/374584
Research Article

A Note on Pseudo-Umbilical Submanifolds of Hessian Manifolds with Constant Hessian Sectional Curvature

Department of Mathematics, Faculty of Arts and Science, Firat University, 23119 Elazig, Turkey

Received 22 March 2011; Accepted 26 April 2011

Academic Editor: S. Sivasubramanian

Copyright © 2011 Münevver Yildirim Yilmaz and Mehmet Bektaş. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The geometry of Hessian manifold, as a branch of statistics, physics, Kaehlerian, and affine differential geometry, is deeply fruitful and a new field for scientists. However, inspite of its importance submanifolds and curvature conditions of it have not been so well known yet. In this paper, we focus on the pseudo-umbilical submanifolds on Hessian manifold with constant Hessian sectional curvature and using sectional curvature conditions we obtain new results on it.