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J. Korean Math. Soc. 2019; 56(4): 1113-1129
Online first article May 17, 2019 Printed July 1, 2019
https://doi.org/10.4134/JKMS.j180642
Copyright © The Korean Mathematical Society.
Riemannian manifolds with a semi-symmetric metric $P$-connection
Sudhakar Kr Chaubey, Jae Won Lee, Sunil Kr Yadav
Shinas College of Technology, Gyeongsang National University; Poornima College of Engineering
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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