On statistical generalized recurrent manifolds

Document Type : Original Article

Authors

1 Department of Mathematics, University of Zanjan, Zanjan, Iran

2 Department of Mathematics ,University of Zanjan, P.O Box 45371-38791, Zanjan, Iran

Abstract

In this paper, we introduce a statistical generalized recurrent manifold, which its curvature tensor
R*, satisfies the generalized recurrent condition ∇*R*=ΓR*+θ H. Next we prove that a statistical generalized recurrent manifold with constant curvature is as same as a generalized recurrent manifold with respect to its Levi-Civita connection.
Also we show that a statistical generalized recurrent manifold is neither statistical semi-symmetric, nor statistical Ricci semi-symmetric. Finally we prove that in spite of the Riemannian manifold, a statistical generalized recurrent manifold is not statistical concircular recurrent.

Keywords

References

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Journal of Finsler Geometry and its Applications
Volume 5, Issue 2
December 2024
Pages 101-115

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