Invariants of Special Second-Type Almost Geodesic Mappings of Generalized Riemannian Space

Abstract

We studied rules of transformations of Christoffel symbols under third type almost geodesic mappings in this paper. From this research, we obtained some new invariants of these mappings. These invariants are analogies of Thomas projective parameter and Weyl projective tensor.

Cosmological meaning of geometric curvatures

“…In the paper Ivanov, Zlatanović [6] , the physical motivation with respect to the Einstein's works [2][3][4] is well explained. Some other papers where these Einstein's works are cited as the motivations for further researches about the spaces with torsion are [15,[19][20][21][22][23] and many others.…”

“…An N-dimensional manifold M N , equipped with a non-symmetric metric tensorˆ of the type (0, 2) whose components are i j is the generalized Riemannian space GR N in the sense of Eisenhart's definition [5] . S. M. Minčić [13][14][15], M. S. Stanković [19,20,22,23], Lj. S. Velimirović [15,19,22], M. Lj.…”

Basic invariants of geometric mappings

“…An N-dimensional manifold M N equipped with an affine connection ∇ (with torsion) is called the non-symmetric affine connection space GA N see [6,[12][13][14][15]18,19,21] . As a special case, the manifold M N equipped with a torsion-free affine connection 0 ∇ is called the symmetric affine connection space A N .…”

On a Ricci quarter-symmetric metric recurrent connection and a projective Ricci quarter-symmetric metric recurrent connection in a Riemannian manifold

“…Afterwards, several types of a quarter-symmetric metric connection were studied ([4, 10, 19, 22]). In [7,14,20,23,24], the geometric and physic properties of conformal and projective the semi-symmetric metric recurrent connections were studied. And in [17,18] a projective conformal quarter-symmetric metric connection and a generalized quarter-symmetric metric recurrent connection were studied.…”