On global geodesic mappings of $n$-dimensional surfaces of revolution

Details On global geodesic mappings of $n$-dimensional surfaces of revolution On global geodesic mappings of $n$-dimensional surfaces of revolution

2011-03-31

arxiv.org/abs/1103.6128v1

Mathematics

Differential Geometry

10 pages

Scientific paper

In this paper we study geodesic mappings of $n$-dimensional surfaces of revolution. From the general theory of geodesic mappings of equidistant spaces we specialize to surfaces of revolution and apply the obtained formulas to the case of rotational ellipsoids. We prove that such $n$-dimensional ellipsoids admit non trivial smooth geodesic deformations onto $n$-dimensional surfaces of revolution, which are generally of a different type.

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