A characterization for totally real submanifolds using self-adjoint differential operator

Abstract

In this article, we study totally real submanifolds in Kaehler product manifold with constant scalar curvature using self-adjoint differential operator □. Under this setup, we obtain a characterization result. Moreover, we discuss δ−invariant properties of such submanifolds and get an obstruction result as an application of the inequality derived. The results in the article are supported by non-trivial examples.

Keywords

• totally real submanifolds
• self-adjoint differential operator
• kaehler product manifold
• δ−invariant