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

TL;DR

This paper investigates geodesic mappings of n-dimensional surfaces of revolution, deriving formulas for rotational ellipsoids and demonstrating their ability to undergo non-trivial smooth deformations into different surface types.

Contribution

It extends the theory of geodesic mappings to n-dimensional surfaces of revolution and provides explicit formulas for rotational ellipsoids, showing their deformability.

Findings

n-dimensional ellipsoids admit non-trivial smooth geodesic deformations

formulas for geodesic mappings of surfaces of revolution derived

ellipsoids can deform into surfaces of different types

Abstract

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.