I. Hinterleitner, N. I. Guseva, J. Mikeš, “On geodesic definiteness by similarity points”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2020, Volume 182,Pages <nobr>19

On geodesic definiteness by similarity points

I. Hinterleitner^a, N. I. Guseva^bc, J. Mikeš^d

^a Institute of Mathematics, Faculty of Mechanical Engeneering, Brno Technical Univercity
^b Moscow State Pedagogical University
^c All-Russian Institute for Scientific and Technical Information of Russian Academy of Sciences, Moscow
^d Palacký University Olomouc

Abstract: In this paper, we present some results obtained in the theory of geodesic mappings of surfaces. It is well known that a mapping that is both conformal and geodesic is homothetic. Based on this property, we obtain new results on the definiteness of surfaces with respect to geodesic mappings, which generalize results obtained by V. T. Fomenko.

Keywords: geodesic mapping, conformal mapping, pseudo-Riemannian space, Riemannian space, surface, definiteness.

UDC: 514.76

MSC: 53B05, 53B20, 53B22, 11Y11

DOI: 10.36535/0233-6723-2020-182-19-27