Compact Totally Real Minimal Submanifolds in a Bochner-Kaehler Manifold

Year 2018, Volume: 1 Issue: 4, 254 - 257, 20.12.2018

Zühal Küçükarslan Yüzbaşı Mehmet Bektaş Münevver Yıldırım Yılmaz

https://doi.org/10.32323/ujma.422271

Cited By: 1

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

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