Pinching Results for Submanifolds in Lorentzian–Sasakian Manifolds Endowed with a Semi-Symmetric Non-Metric Connection

Abstract

We establish an improved Chen inequality involving scalar curvature and mean curvature and geometric inequalities for Casorati curvatures, on slant submanifolds in a Lorentzian–Sasakian space form endowed with a semi-symmetric non-metric connection. Also, we present examples of slant submanifolds in a Lorentzian–Sasakian space form.

Keywords

• Chen invariants
• Chen inequalities
• Casorati curvature
• Lorentzian–Sasakian manifold
• semi-symmetric connection
• non-metric connection