Optimal Inequalities on (<i>α</i>,<i>β</i>)-Type Almost Contact Manifold with the Schouten–Van Kampen Connection

Abstract

In the current research, we develop optimal inequalities for submanifolds in trans-Sasakian manifolds or (α,β)-type almost contact manifolds endowed with the Schouten–Van Kampen connection (SVK-connection), including generalized normalized δ-Casorati Curvatures (δ-CC). We also discuss submanifolds on which the equality situations occur. Lastly, we provided an example derived from this research.

Keywords

• trans-Sasakian manifold
• Casorati Curvature
• scalar curvature
• Schouten–Van Kampen connection
• submanifolds
• second fundamental form