On global geodesic mappings of nn-dimensional surfaces of revolution

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.Comment: 10 page

On F-planar mappings of spaces with affine connections

In this paper we study F-planar mappings of n-dimensional or infinitely dimensional spaces with a torsion-free affine connection. These mappings are certain generalizations of geodesic and holomorphically projective mappings. Here we make fundamental equations on F-planar mappings for dimensions $n>2$ more precise

On geodesic mappings of manifolds with affine connection

In this paper we prove that all manifolds with affine connection are globally projectively equivalent to some space with equiaffine connection (equiaffine manifold). These manifolds are characterised by a symmetric Ricci tensor.Comment: 5 page

There Are No Conformal Einstein Rescalings of Pseudo-Riemannian Einstein Spaces with n Complete Light-Like Geodesics

In the present paper, we study conformal mappings between a connected n-dimension pseudo-Riemannian Einstein manifolds

Mercator’s Projection – a Breakthrough in Maritime Navigation

This paper is focused on Mercator’s projection as a breakthrough in maritime navigation. In the paper, the principle and properties of Mercator’s projection are described. The advantages, disadvantages and current utilization are mentioned

Geodesic Mappings of Spaces with Affine Connections onto Generalized Symmetric and Ricci-Symmetric Spaces

In the paper, we consider geodesic mappings of spaces with an affine connections onto generalized symmetric and Ricci-symmetric spaces. In particular, we studied in detail geodesic mappings of spaces with an affine connections onto 2-, 3-, andm- (Ricci-) symmetric spaces. These spaces play an important role in the General Theory of Relativity. The main results we obtained were generalized to a case of geodesic mappings of spaces with an affine connection onto (Ricci-) symmetric spaces. The main equations of the mappings were obtained as closed mixed systems of PDEs of the Cauchy type in covariant form. For the systems, we have found the maximum number of essential parameters which the solutions depend on. Anym- (Ricci-) symmetric spaces (m >= 1) are geodesically mapped onto many spaces with an affine connection. We can call these spacesprojectivelly m- (Ricci-) symmetric spacesand for them there exist above-mentioned nontrivial solutions