Deviation equations in spaces with affine connection

Differential Geometry - Dynamical Systems

1 We develop the method of anholonomic frames with associated nonlinear connection (in brief, N–connection) structure and show explicitly how geometries with local anisotropy (various type of Finsler–Lagrange–Cartan–Hamilton spaces) can be modelled on the metric–affine spaces. There are formulated the criteria when such generalized Finsler metrics are effectively defined in the Einstein, telepa...

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

In 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 GRN , where GRN has a non-symmetric metric tensor, i.e. we study the case when GAN and GRN have the same to...

Special equitorsion almost geodesic mappings of the third type of non-symmetric affine connection spaces

In this paper we investigate a special kind of almost geodesic mapping of the third type of spaces with non-symmetric affine connection. Also we find some relations for curvature tensors of associated affine connection spaces of almost geodesic mappings of the third type. Finally, we investigate equitorsion almost geodesic mapping having the property of reciprocity and find an invariant geometr...

Deviation Equations of Synge and Schild over (l N , G)-spaces

Deviation equation of Synge and Schild has been investigated over dif-ferentiable manifolds with contravariant and covariant affine connections (whose components differ not only by sign) and metric [(Ln, g)-spaces]. It is shown that the condition £ ξ u = 0 for obtaining this equation is only a sufficient (but not necessary) condition. By means of a non-isotropic (non-null) vector field u [g(u, ...

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition