Geodesic
Investigations on a Riemannian Manifold with a Semi-Symmetric Non-Metric Connection and Gradient Solitons
Kragujevac Journal of Mathematics, Tome 49 (2025) no. 3, p. 387

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This article carries out the investigation of a three-dimensional Riemannian manifold $N^3$ 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 $N^{3}$. It is established that a $N^3$ 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 $N^3$ with the semi-symmetric type non-metric connection is a gradient Yamabe soliton, then either $N^{3}$ 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 $N^3$ with a semi-symmetric type non-metric connection whose metrics are Einstein solitons and $m$-quasi Einstein solitons of gradient type, respectively.
Classification : 53C05, 53C20, 53C25
Keywords: Riemannian manifolds, gradient Ricci solitons, gradient Yamabe solitons, gradient Einstein solitons, $m$-quasi Einstein solitons 
Krishnendu De; Uday C; and De; Aydin Gezer. Investigations on a Riemannian Manifold with a Semi-Symmetric Non-Metric Connection and Gradient Solitons. Kragujevac Journal of Mathematics, Tome 49 (2025) no. 3, p. 387 . http://geodesic.mathdoc.fr/item/KJM_2025_49_3_a4/
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     author = {Krishnendu De and Uday C and and De and Aydin Gezer},
     title = {Investigations on a {Riemannian} {Manifold} with a {Semi-Symmetric} {Non-Metric} {Connection} and {Gradient} {Solitons}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {387 },
     year = {2025},
     volume = {49},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2025_49_3_a4/}
}
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