论文信息 - On geodesic mappings of equidistant generalized Riemannian spaces

On geodesic mappings of equidistant generalized Riemannian spaces

Abstract In this paper geodesic mappings of equidistant generalized Riemannian spaces are discussed. It is proved that each equidistant generalized Riemannian space of basic type admits non-trivial geodesic mapping with preserved equidistant congruence. Especially, there exists non-trivial geodesic mapping of equidistant generalized Riemannian space onto equidistant Riemannian space. An example of geodesic mapping of an equidistant generalized Riemannian spaces is presented.

[1] G. Hall,et al. Projective equivalence of Einstein spaces in general relativity , 2009 .

[2] Milan Lj. Zlatanovic. On equitorsion geodesic mappings of general affine connection spaces onto generalized Riemannian spaces , 2011, Appl. Math. Lett..

[3] M. Stankovic,et al. Equitorsion geodesic mappings of generalized Riemannian spaces. , 1997 .

[4] Luther Pfahler Eisenhart,et al. Non-Riemannian Geometry , 2005 .

[5] L. Eisenhart. Generalized Riemann Spaces. , 1951, Proceedings of the National Academy of Sciences of the United States of America.

[6] I. Hinterleitner,et al. On geodesic mappings of manifolds with affine connection , 2009, 0905.1839.

[7] G. Hall,et al. The principle of equivalence and projective structure in spacetimes , 2007, gr-qc/0703104.

[8] J. Mikeš,et al. Projective equivalence and manifolds with equiaffine connection , 2011 .

[9] K. Yano. Concircular Geometry I. Concircular Transformations , 1940 .