Pinching Theorems for a Vanishing C-Bochner Curvature Tensor

Abstract

The main purpose of this article is to construct inequalities between a main intrinsic invariant (the normalized scalar curvature) and an extrinsic invariant (the Casorati curvature) for some submanifolds in a Sasakian manifold with a zero C-Bochner tensor.

Keywords

• C-Bochner tensor
• generalized normalized <i>δ</i>-Casorati curvature
• Sasakian manifold
• slant
• invariant
• anti-invariant