XXXV Workshop on Geometric Methods in Physics 26.06-2.07.2016

Volodymyr Berezovski

Almost geodesic mappings

We and J. Mikes give some conditions preserved Riemannian curvature tensor with respect to almost geodesic mappings of affinely connected spaces. It is noteworthy that these conditions are valid for other types of mappings. For the almost geodesic mappings of first type, when the Riemannian curvature tensor is invariant, the authors deduce a differential equations system of Cauchy type.
In addition the authors investigate almost geodesic mappings of first type,
where the Weyl tensor of projective curvature is invariant and Riemannian
tensor is not invariant.

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