Anti-Invariant Lorentzian Submersions From Lorentzian Concircular Structure Manifolds

Abstract

This research article attempts to investigate anti-invariant Lorentzian submersions and the Lagrangian Lorentzian submersions (LLS) from the Lorentzian concircular structure [in short (LCS)n] manifolds onto semi-Riemannian manifolds with relevant non-trivial examples. It is shown that the horizontal distributions of such submersions are not integrable and their fibers are not totally geodesic. As a result, they can not be totally geodesic maps. Anti-invariant and Lagrangian submersions are also explored for their harmonicity. We illustrate that if the Reeb vector field is horizontal, the anti-invariant and LLS can not be harmonic.

Curves Along Lorentzian Submersions

“…A Lorentzian submersion is a smooth map between two Lorentzian manifolds that preserves the Lorentzian metric, meaning that the pullback metric of the submersion is equal to the metric on the domain manifold. Semi-Riemannian submersions have become a fascinating topic of research due to their applications in mathematical physics, particularly in the theory of relativity, as well as in Yang-Mills theory, string theory, Kaluza-Klein theory, Hodge theory, and other related areas [16]. Semi-Riemannian submersions also have applications in mathematical physics, particularly in the study of Einstein's theory of general relativity and they can be used to describe the geometry of spacetime, as well as the behavior of gravitational waves and black holes.…”