Study on Ricci curvature tensor under conformal transformation

Abstract

This study explores the behavior of the Ricci tensor under conformal transformations of Riemannian manifolds. Conformal transformations, which preserve angles but not lengths, play a pivotal role in differential geometry and theoretical physics, particularly in the context of conformal geometry and general relativity. These analyze how the Ricci tensor transforms when the metric tensor undergoes a conformal transformation. The analysis of the Ricci tensor to conformal transformations studies how curvature responds to the resizing of the metric tensor and is of fundamental importance to the study of geometric structures and physical phenomena in general relativity, cosmology, and conformal field theory.