On equitorsion geodesic mappings of general affine connection spaces onto generalized Riemannian spaces

AbstractIn the papers Minčić (1973) [15], Minčić (1977) [16], several Ricci type identities are obtained by using non-symmetric affine connection. Four kinds of covariant derivatives appear in these identities.In the present work, we consider equitorsion geodesic mappings f of two spaces GAN and GR¯N, where GR¯N has a non-symmetric metric tensor, i.e. we study the case when GAN and GR¯N have the same torsion tensors at corresponding points. Such a mapping is called an equitorsion mapping Minčić (1997) [12], Stanković et al. (2010) [14], Stanković (in press) [13].The existence of a mapping of such type implies the existence of a solution of the fundamental equations. We find several forms of these fundamental equations. Among these forms a particularly important form is system of partial differential equations of Cauchy type

Equitorsion holomorphically projective mappings of generalized Kählerian space of the first kind

summary:In this paper we define generalized Kählerian spaces of the first kind $(G\underset 1K_N)$ given by (2.1)--(2.3). For them we consider hollomorphically projective mappings with invariant complex structure. Also, we consider equitorsion geodesic mapping between these two spaces ($G\underset 1K_N$ and $G\underset 1{\overline K}_N$) and for them we find invariant geometric objects

Basic invariants of geometric mappings

This study is motivated by the researches in the field of invariants of geodesic and conformal mappings presented in (T. Y. Thomas, [22]) and (H. Weyl, [25]). The Thomas projective parameter and the Weyl projective tensor are generalized in this article. Generators for vector spaces of invariants of geometric mappings are obtained in here

Novel invariants for almost geodesic mappings of the third type

Two kinds of invariance for geometrical objects under transformations are involved in this paper. With respect to these kinds, we obtained novel invariants for almost geodesic mappings of the third type of a non-symmetric affine connection space in this paper. Our results are presented in two sections. In the Section 3, we obtained the invariants for the equitorsion almost geodesic mappings which do not have the property of reciprocity. In the Section 4, we obtained the invariants for almost geodesic mappings of the third type which have the property of reciprocity.Comment: 18 pages, 0 figure

SOME NEW IDENTITIES FOR THE SECOND COVARIANT DERIVATIVE OF THE CURVATURE TENSOR

In this paper we study the second covariant derivative of Riemannian curvature tensor. Some new identities for the second covariant derivative are given. Namely, identities obtained by cyclic sum with respect to three indices are given. In the first case, two curvature tensor indices and one covariant derivative index participate in the cyclic sum, while in the second case one curvature tensor index and two covariant derivative indices participate in the cyclic sum