Some properties of ET-projective tensors obtained from Weyl projective tensor

Abstract

Vanishing of linearly independent curvature tensors of a non-symmetric affine connection space as functions of vanished curvature tensor of the associated space of this one are analyzed in the first part of this paper. Projective curvature tensors of a non-symmetric affine connection space are expressed as functions of the affine connection coefficients and Weyl projective tensor of the corresponding associated affine connection space in the second part of this paper.

Semi-Symmetric Metric Connection on Homothetic Kenmotsu Manifolds

“…In a Riemannian manifold 2 +1 , if there exist a one-to-one correspondence between each coordinate neighborhood of 2 +1 and a domain in Euclidean space such that any geodesic of the Riemannian manifold corresponds to a straight line in the Euclidean space then 2 +1 is said to be locally projectively flat. For recent developments on projective curvature tensor, we refer [18,19]. ∇ 2 1 = 0, ∇ 2 2 = − 1 3 , ∇ 2 3 = − − 1 2 , ∇ 3 1 = 0, ∇ 3 2 = 0, ∇ 3 3 = 0.…”

Weyl projective objects $\protect\underset{1}{\mathcal{W}}, \underset{2}{\mathcal{W}},\underset{3}{\mathcal{W}}$ for equitorsion geodesic mappings

“…for a 1-form and an anti-symmetric tensor of the type (0,2). Invariants of geodesic mappings of a non-symmetric affine connection manifold GA N and some their properties are obtained in [25][26][27]. The main goal of this paper is to obtain some other generalizations of invariants of geodesic mappings defined on the manifold GA N .…”

“…GA N be an equitorsion geodesic mapping of a non-symmetric affine connection manifold GA N . The basic equation of this mapping is (see [25][26][27])…”

“…Many research papers and monographs [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][21][22][23][24][25][26][27] are focused on development of the affine connection spaces theory, on the theory of mappings between these spaces, on the theory of invariants of these mappings and on the applications of them. N. S. Sinyukov [21], J. Mikeš with his research group [9][10][11]22], G. Hall [6,7], G. P. Pokhariyal [16,17], U. P. Singh [20] and many other researchers have given significant contributions to the development of the concept of symmetric affine connection spaces.…”

Riemannian manifolds satisfying certain conditions on pseudo-projective curvature tensor

“…Hence the projective curvature tensor is the measure of the failure of a Riemannian manifold to be of constant curvature. For recent developments on projective curvature tensor, we refer to [16] and [21].…”