SINGULARITIES OF GEODESIC FLOWS AND GEODESIC LINES IN PSEUDO-FINSLER SPACES. I

Cover Page

Cite item

Full Text

Abstract

This is a first paper in the series devoted to singularities of geodesic flows in generalized Finsler (pseudo-Finsler) spaces. Geodesics are defined as extremals of a certain auxiliary functional whose non-isotropic extremals coincide with extremals of the action functional. This allows to consider isotropic lines as (unparametrized) geodesics, similarly to pseudo-Riemannian metrics. In the next forthcoming paper we study generic singularities of sodefined geodesic flows in the case when the pseudo-Finsler metric is given by a generic 3-form on a two-dimensional manifold.

About the authors

Aleksei Nikolaevich Kurbatskiy

Moscow Lomonosov State University

Email: akurbatskiy@gmail.com
Candidate of Physics and Mathematics, Associate Professor of the Department of Econometrics and Mathematical Methods of Economics Moscow, the Russian Federation

Natalia Gennadievna Pavlova

Peoples’ Friendship University of Russia

Email: natasharussia@mail.ru
Candidate of Physics and Mathematics, Associate Professor of the Department of Nonlinear Analysis and Optimization Moscow, the Russian Federation

Aleksei Olegovich Remizov

Trapeznikov Institute of Control Sciences of RAS

Email: alexey-remizov@yandex.ru
Candidate of Physics and Mathematics, Researcher of the Laboratory of Qualitative Analysis for Nonlinear Dynamic Systems Moscow, the Russian Federation

References

  1. Ghezzi R., Remizov A. O. On a class of vector fields with discontinuities of divide-by-zero type and its applications to geodesics in singular metrics // Journal of Dynamical and Control Systems, 2012. V. 18. № 1. P. 135-158.
  2. Павлова Н. Г., Ремизов А. О. Геодезические на гиперповерхностях в пространстве Минковского: особенности смены сигнатуры // УМН, 2011. Т. 66. № 6 (402). С. 193-194.
  3. Ремизов А. О. Геодезические на двумерных поверхностях с псевдоримановой метрикой: особенности смены сигнатуры // Матем. сб. 2009. Т. 200. № 3. С. 75-94.
  4. Remizov A. O. On the local and global properties of geodesics in pseudo-Riemannian metrics // Differential Geometry and its Applications. 2015. V. 39. P. 36-58.
  5. Рунд Х. Дифференциальная геометрия финслеровых пространств. М.: Наука, 1981.
  6. Balan V., Neagu M. Jet single-time Lagrange geometry and its applications // John Wiley & Sons, Inc., Hoboken, NJ, 2011.
  7. Matsumoto M., Shimada H. On Finsler spaces with 1-form metric. II. Berwald-Moor’s metric // Tensor (N.S.). 1978. V. 32. № 3. P. 275-278.
  8. Bao D., Chern S.-S., Shen Z. An Introduction to Riemann-Finsler Geometry // Graduate Texts in Mathematics, 200. Springer-Verlag, New York, 2000.
  9. Matsumoto M. Two-dimensional Finsler spaces whose geodesics constitute a family of special conic sections // J. Math. Kyoto Univ., 1995. V. 35. № 3. P. 357-376.
  10. Mikes J., Hinterleitner I., Vanzurova A. One remark on variational properties of geodesics in pseudoriemannian and generalized Finsler spaces // In: Geometry, integrability and quantization, Softex, Sofia, 2008. P. 261-264.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Согласие на обработку персональных данных

 

Используя сайт https://journals.rcsi.science, я (далее – «Пользователь» или «Субъект персональных данных») даю согласие на обработку персональных данных на этом сайте (текст Согласия) и на обработку персональных данных с помощью сервиса «Яндекс.Метрика» (текст Согласия).