Riemannian manifolds with a semi-symmetric metric $P$-connection
J. Korean Math. Soc. 2019 Vol. 56, No. 4, 1113-1129
Published online July 1, 2019
Sudhakar Kr Chaubey, Jae Won Lee, Sunil Kr Yadav
Shinas College of Technology, Gyeongsang National University; Poornima College of Engineering
Abstract : We define a class of semi-symmetric metric connection on a Riemannian manifold for which the conformal, the projective, the concircular, the quasi conformal and the $m$-projective curvature tensors are invariant. We also study the properties of semisymmetric, Ricci semisymmetric and Eisenhart problems for solving second order parallel symmetric and skew-symmetric tensors on the Riemannian manifolds equipped with a semi-symmetric metric $P$-connection.
Keywords : Riemannian manifolds, second order parallel tensors, Ricci solitons, symmetric spaces, semi-symmetric metric connection, different curvature tensors
MSC numbers : 53D10, 53C25, 53D15
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