Lorentzian manifolds: A characterization with a type of semi-symmetric non-metric connection

초록

This paper characterizes the Lorentzian manifolds endowed with a semi-symmetric non-metric rho-connection (briefly, ssnm rho c). First, the existence of semi-symmetric non-metric connection (ssnmc) on Lorentzian manifold is established, and it is shown that an n-dimensional Lorentzian manifold equipped with an ssnm rho c is a generalized Robertson-Walker spacetime. We also establish the condition for a Lorentzian manifold together with an ssnm rho c to be a Robertson-Walker spacetime. In this series, the properties of Ricci semi-symmetric Lorentzian manifold endowed with an ssnm rho c, almost Ricci solitons and gradient Ricci solitons are explored. Finally, a non-trivial example of Lorentzian manifold admits an ssnm rho c, which is constructed to verify some of our results.

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