Investigations on a Riemannian Manifold with a Semi- Symmetric Non-Metric Connection and Gradient Solitons
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Authors: K. DE, U. C. DE AND A. GEZER
DOI: 10.46793/KgJMat2503.387D
Abstract:
This article carries out the investigation of a three-dimensional Riemannian manifold N3 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 N3. It is established that a N3 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 N3 with the semi-symmetric type non-metric connection is a gradient Yamabe soliton, then either N3 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 N3 with a semi-symmetric type non-metric connection whose metrics are Einstein solitons and m-quasi Einstein solitons of gradient type, respectively.
Keywords:
Riemannian manifolds, gradient Ricci solitons, gradient Yamabe solitons, gradient Einstein solitons, m-quasi Einstein solitons.
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