Symmetry and Curvature in LP-Kenmotsu Manifolds with Generalized Tanaka-Webster Connection

Abstract

In this study, we investigate Lorentzian para-Kenmotsu (LP-Kenmotsu (LPK)) manifolds in the context of the generalized Tanaka-Webster connection, denoted as $\mathcal{D}^*$. Initially, we derive the formulas for the curvature tensor, Ricci tensor, and scalar curvature of an LPK manifold with respect to the connection $\mathcal{D}^*$. We analyze the geometric properties of these manifolds, including their local symmetry, Ricci semi-symmetry, and local $\psi$-symmetry. Furthermore, utilizing the $Q$-curvature tensor, we analyze conditions under which LPK manifolds exhibit ${Q^*}$-flatness, ${Q^*}$-Ricci semi-symmetry, and $\psi$-${Q^*}$-flatness concerning the connection $\mathcal{D}^*$

Keywords

• Lorentzian para-Kenmotsu manifolds
• Generalized Tanaka-Webster Connection
• Einstein manifold
• $Q$-curvature tensor

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