Paper · Feb 24, 2024
Investigations on a Riemannian manifold with a semi-symmetric non-metric connection and gradient solitons
As on arXiv
Abstract
This article carries out the investigation of a three-dimensional Riemannian manifold endowed with a semi-symmetric type non-metric connection. Firstly, we construct a non-trivial example to prove the existence of a semi-symmetric type non-metric connection on . It is established that a with the semi-symmetric type non-metric connection, whose metric is a gradient Ricci soliton, is a manifold of constant sectional curvature with respect to the semi-symmetric type non-metric connection. Moreover, we prove that if the Riemannian metric of with the semi-symmetric type non-metric connection is a gradient Yamabe soliton, then either is a manifold of constant scalar curvature or the gradient Yamabe soliton is trivial with respect to the semi-symmetric type non-metric connection. We also characterize the manifold with a semi-symmetric type non-metric connection whose metrics are Einstein solitons and -quasi Einstein solitons of gradient type, respectively.
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Background reading
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In the guidebook
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