Wintgen Inequalities for Submanifolds of $\delta$-Lorentzian Trans-Sasakian Space Form

Abstract

The outline of this research article is that, $\delta$-Lorentzian trans Sasakian manifolds with a semi-symmetric-metric connection (briefly say $SSM$) have been investigated. Indeed, we obtain the expressions for Riemannian curvature tensor $\bar{R}$, Ricci curvature tensors $\bar{Ric}$ and scalar curvature $\bar{r}$ of the $\delta$-Lorentzian trans-Sasakian manifolds with a $SSM$ connection. Mainly, we discuss the generalized Wintgen inequalities for submanifolds in $\delta$-Lorentzian trans-Sasakian space form with a $SSM$ connection. Furthermore, we examine the generalized Wintgen inequality for submanifolds of $\delta$-Lorentzian trans-Sasakian space form.

Keywords

• $\delta$-Lorentzian trans-Sasakian manifold
• semi-symmetric metric connection
• Wintgen inequalities

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