On Geodesic Definiteness by Similarity Points

被引：0
作者：
Hinterleitner I. [1 ]
Guseva N.I. [2 ,3 ]
Mikeš J. [4 ]
机构：
[1] Brno University of Technology, Brno
[2] Moscow Pedagogical State University, Moscow
[3] Russian Institute for Scientific and Technical Information of the Russian Academy of Sciences, Moscow
[4] Palacký University Olomouc, Olomouc
来源：
Journal of Mathematical Sciences | 2023年 / 277卷 / 5期
关键词：
11Y11; 53B05; 53B20; 53B22; conformal mapping; definiteness; geodesic mapping; pseudo-Riemannian space; Riemannian space; surface;
D O I：
10.1007/s10958-023-06879-z
中图分类号：
学科分类号：
摘要：
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. © 2023, Springer Nature Switzerland AG.
引用
收藏
页码：727 / 735
页数：8
相关论文
共 53 条
  • [1] Afwat M., Svec A., Global differential geometry of hypersurfaces, Rozpr. Česk. Akad. Věd, Řada Mat. Přír. Věd., 88, 7, (1978)
  • [2] Berezovskii V.E., Guseva N.I., Mikes J., On a particular case of first-type almost geodesic mappings of affinely connected spaces that preserve a certain tensor, Mat. Zametki, 98, 3, pp. 463-466, (2015)
  • [3] Berezovskii V.E., Hinterleitner I., Guseva N.I., Mikes J., Conformal mappings of Riemannian spaces onto Ricci symmetric spaces, Mat. Zametki, 103, 2, pp. 303-306, (2018)
  • [4] Chuda H., Mikes J., First Quadratic Integral of Geodesics with Certain Initial Conditions, pp. 85-88, (2007)
  • [5] Chuda H., Mikes J., Conformally geodesic mappings satisfying a certain initial condition, Arch. Math. (Brno), 47, pp. 389-394, (2011)
  • [6] Ciric M., Zlatanovic M., Stankovic M., Velimirovic L., On geodesic mappings of equidistant generalized Riemannian spaces, Appl. Math. Comput., 218, pp. 6648-6655, (2012)
  • [7] Dini U., On a problem in the general theory of the geographical representations of a surface on another, Anal. Mat., 3, pp. 269-294, (1869)
  • [8] Eisenhart L.P., Riemannian Geometry, Princeton Univ, (1926)
  • [9] Evtushik L.E., Hinterleitner I., Guseva N.I., Mikes J., Conformal mappings onto Einstein spaces, Izv. Vyssh. Ucheb. Zaved. Mat., 10, pp. 8-13, (2016)
  • [10] Fomenko V.T., On the unique determination of closed surfaces with respect to geodesic mappings, Dokl. Ross. Akad. Nauk, 407, 4, pp. 453-456, (2006)
123456