Analytical exploration of weyl-conformal curvature tensor in Lorentzian β-Kenmotsu manifolds endowed with generalized Tanaka-Webster connection

Abstract

This paper investigates the conformal curvature properties of Lorentzian β-Kenmotsu (LβK) manifolds admitting a generalized Tanaka-Webster (g-TW) connection. We begin by establishing the fundamental preliminaries of LβK manifolds and exploring their curvature properties under the influence of g-TW connection. The study then focuses on specific curvature conditions, including R· S = 0, S· R = 0, conformally flat, ζ-conformally flat, and pseudo-conformally flat conditions, to examine their geometric and structural implications. Additionally, we construct an explicit example of a 3-dimensional LβK manifold that admits a g-TW connection, providing concrete validation of our theoretical results. The findings contribute to the broader understanding of curvature behaviors in almost contact pseudo-Riemannian geometry and extend the study of non-Riemannian connections in Lorentzian manifolds.