Journal of the
Korean Mathematical Society JKMS

In this article, we establish sharp relations between the sectional curvature and the shape operator and also between the $k$-Ricci curvature and the shape operator for a totally real submanifold in a locally conformal Kaehler space form of constant holomorphic sectional curvature with arbitrary codimension.

Keywords: mean curvature, sectional curvature, shape operator, $k$-Ricci curvature, locally conformal Kaehler space form, totally real submanifold

MSC numbers: 53B25, 53B35, 53C40