- Universal Journal of Mathematics and Applications
- Vol: 1 Issue: 4
- Compact Totally Real Minimal Submanifolds in a Bochner-Kaehler Manifold
Compact Totally Real Minimal Submanifolds in a Bochner-Kaehler Manifold
Authors : Zühal Küçükarslan Yüzbaşi, Mehmet Bektaş, Münevver Yildirim Yilmaz
Pages : 254-257
Doi:10.32323/ujma.422271
View : 10 | Download : 3
Publication Date : 2018-12-20
Article Type : Research
Abstract :In this paper, we establish the following results: Let $M$ be an $% m-$dimensional compact totally real minimal submanifold immersed in a locally symmetric Bochner-Kaehler manifold $\tilde{M}$ with Ricci curvature bounded from below. Then either $M$ is a totally geodesic or \begin{equation*} \inf r\leq \frac{1}{2}\left( \frac{1}{2}m\left( m-1\right) \tilde{k}-\frac{1% }{3}\left( m+1\right) \tilde{c}\right), \end{equation*}% where $r$ is the scalar curvature of $M.$Keywords : Bochner-Kaehler manifold, Ricci curvature