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 : 18 | Download : 8

Publication Date : 2018-12-20

Article Type : Research Paper

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}\leftinsert ignore into journalissuearticles values( \frac{1}{2}m\leftinsert ignore into journalissuearticles values( m-1\right); \tilde{k}-\frac{1% }{3}\leftinsert ignore into journalissuearticles values( m+1\right); \tilde{c}\right);, \end{equation*}% where $r$ is the scalar curvature of $M.$
Keywords : Bochner Kaehler manifold, Ricci curvature