Characterizations of Lorentzian manifolds

초록

The focus of this paper is to characterize the Lorentzian manifolds equipped with a semi-symmetric non-metric rho-connection [briefly, (M, backward difference ~)]. The conditions for a Lorentzian manifold to be a generalized Robertson-Walker spacetime are established and vice versa. We prove that an n-dimensional compact (M, backward difference ~) is geodesically complete. We also study the properties of almost Ricci solitons and gradient almost Ricci solitons on Lorentzian manifolds and Yang pure space, respectively. Finally, we study the properties of semisymmetric (M, backward difference ~), and it is proven that (M, backward difference ~ ) is semisymmetric if and only if it is a Robertson-Walker spacetime. Published under an exclusive license by AIP Publishing.

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