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http://dx.doi.org/10.4134/CKMS.c210046

STUDY OF GRADIENT SOLITONS IN THREE DIMENSIONAL RIEMANNIAN MANIFOLDS  

Biswas, Gour Gopal (Department of Mathematics University of Kalyani)
De, Uday Chand (Department of Pure Mathematics University of Calcutta)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.3, 2022 , pp. 825-837 More about this Journal
Abstract
We characterize a three-dimensional Riemannian manifold endowed with a type of semi-symmetric metric P-connection. At first, it is proven that if the metric of such a manifold is a gradient m-quasi-Einstein metric, then either the gradient of the potential function 𝜓 is collinear with the vector field P or, λ = -(m + 2) and the manifold is of constant sectional curvature -1, provided P𝜓 ≠ m. Next, it is shown that if the metric of the manifold under consideration is a gradient 𝜌-Einstein soliton, then the gradient of the potential function is collinear with the vector field P. Also, we prove that if the metric of a 3-dimensional manifold with semi-symmetric metric P-connection is a gradient 𝜔-Ricci soliton, then the manifold is of constant sectional curvature -1 and λ + 𝜇 = -2. Finally, we consider an example to verify our results.
Keywords
Ricci soliton; gradient Ricci soliton; gradient m-quasi-Einstein metric; gradient ${\rho}$-Einstein soliton; ${\eta}$-Ricci soliton; gradient ${\eta}$-Ricci soliton; semi-symmetric metric connection; semi-symmetric metric P-connection;
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Times Cited By KSCI : 3  (Citation Analysis)
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