Abstract
We define a semi-symmetric connection on a Weyl manifold and study projective curvature tensor and conformal curvature tensor after giving some properties of the curvature tensor with respect to semi-symmetric connection.
Highlights
Hayden [1] introduced semi-symmetric metric connection on a Riemannian manifold and this definition was developed by Yano [2] and Imai [3,4].In this paper, we define a semi-symmetric connection on a Weyl manifold and define the curvature tensor with respect to semi-symmetric connection
Corollary 2.1: If S i is gradient on a Weyl manifold with semi-symmetric connection, the followings hold: (i)
Theorem 3.2: Projective curvature tensors with respect to semi-symmetric connection and symmetric connection are related with the following relation: ( ) W i jkl
Summary
Hayden [1] introduced semi-symmetric metric connection on a Riemannian manifold and this definition was developed by Yano [2] and Imai [3,4]. After defining projective curvature tensor and conformal curvature tensor with respect to semi-symmetric connection,we obtain some theorems by using properties of these tensors. An n-dimensional manifold which has a symmetric connection and a conformal metric tensor gij is said to be Weyl manifold , if the compatible condition is in the form of ∇ k g ij − 2g ijTk = 0. In this case, Weyl manifold is denoted by Wn ( gij , Tk ). A generalized connection on a Weyl manifold is given by [6]
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