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article · Journal of Mathematical Physics · 2003

Geodesic compatibility and integrability of geodesic flows

Peter Topalov

Cited by 20Abstract and details only

Abstract

We give a natural geometric condition called geodesic compatibility that implies the existence of integrals in involution of the geodesic flow of a pseudo-Riemannian metric. We prove that if two metrics satisfy the condition of geodesic compatibility then we can produce a hierarchy of metrics that also satisfy this condition. A lot of metrics studed in Riemannian and Kählerian geometry satisfy such conditions. We apply our results for obtaining an infinite family (hierarchy) of completely integrable flows on the complex projective plane CPn.

Cite this paper

APA 7

Topalov, P. (2003). Geodesic compatibility and integrability of geodesic flows. Journal of Mathematical Physics, 44(2), 913–929. https://doi.org/10.1063/1.1526939

MLA 9

Topalov, Peter. “Geodesic compatibility and integrability of geodesic flows.” Journal of Mathematical Physics, vol. 44, no. 2, 2003, pp. 913–29, https://doi.org/10.1063/1.1526939.

Chicago

Topalov, Peter. 2003. “Geodesic compatibility and integrability of geodesic flows.” Journal of Mathematical Physics 44 (2): 913–29. https://doi.org/10.1063/1.1526939.

Harvard

Topalov, P. (2003) ‘Geodesic compatibility and integrability of geodesic flows’, Journal of Mathematical Physics, 44(2), pp. 913–929. Available at: https://doi.org/10.1063/1.1526939.

BibTeX
@article{topalov2003geodesic,
  title = {{Geodesic compatibility and integrability of geodesic flows}},
  author = {Topalov, Peter},
  journal = {Journal of Mathematical Physics},
  volume = {44},
  number = {2},
  pages = {913--929},
  year = {2003},
  doi = {10.1063/1.1526939}
}

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