On almost geodesic mappings of the second type between manifolds with non-symmetric linear connection

Abstract

We derive two mixed systems of Cauchy type in covariant derivatives of the first and second kind that ensures the existence of almost geodesic mappings of the second type between manifolds with non-symmetric linear connection. Also, we consider a particular class of these mappings determined by the condition ∇F = 0, where ∇ is the symmetric part of non-symmetric linear connection ∇ 1 and F is the affinor structure. The same special class of almost geodesic mappings of the second type between generalized Riemannian spaces was recently considered in the paper M.Z. Petrović, Special almost geodesic mappings of the second type between generalized Riemannian spaces, Bull. Malays. Math. Sci. Soc. (2),

Canonical almost geodesic mappings of type $\underset\theta\pi{}_2(0,F)$, ${\small\theta\in\{1,2\}}$ between generalized parabolic K\"ahler manifolds

“…Almost geodesic mappings of manifolds with non-symmetric linear connection, which satisfy the property of reciprocity are investigated in [15,19,21,22]. A necessary and sufficient condition for an almost geodesic mapping f W M !…”

“…Almost geodesic mappings of type 2 .e/; e D˙1, from spaces with affine connection onto Riemannian spaces are considered in [10,23], while the paper [5] is dedicated to canonical almost geodesic mappings of type 2 .e D 0/ between Riemannian spaces with an almost affinor structure, and between parabolic Kählerian spaces, particularly. Several papers are devoted to almost geodesic mappings of type  2 .e Ḋ 1/,  2 f1; 2g and its special cases  2 .e D˙1; F /,  2 f1; 2g between manifolds with non-symmetric affine connection, see [15,19,21]. In the papers [16,22] some invariant geometric objects with respect to special almost geodesic mappings of type , respectively, are examined, by considering equitorsion mappings.…”

“…In the papers [16,22] some invariant geometric objects with respect to special almost geodesic mappings of type , respectively, are examined, by considering equitorsion mappings. In [15] we presented systems of differential equations of Cauchy type for almost geodesic mappings of the second type of manifolds with non-symmetric linear connection, also we found some invariant geometric object of almost geodesic mappings of type  2 .e D 1; F /,  2 f1; 2g under some assumptions. In the present paper, we extend and improve results from [5].…”

“…CS.X;Y;Z/A.X; Y; Z/ D A.X; Y; Z/ C A.Y; Z; X / C A.Z; X; Y /:A diffeomorphism f W M ! Mis an almost geodesic mapping of the kind Â; Â 2 f1; 2g if and only if[15] …”

On Conformal and Concircular Diffeomorphisms of Eisenhart’s Generalized Riemannian Spaces

“…Some physical characteristics of conformal mappings were given in [5]. Geodesic mappings and their generalizations is an active research field, see for instance [6][7][8][9][10][11][12][13][14][15]. Some conformal and projective invariants of Riemannnian manifolds were obtained by Reference [16,17].…”