Topalov, P (2002). Geodesically compatible metrics. Existence of commutative conservation laws. Cubo Matemática Educacional, 4(2):371-399.
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. We apply our results for obtaining an infinite family (hierarchy) of completely integrable flows on the complex projective plane CPn.
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. We apply our results for obtaining an infinite family (hierarchy) of completely integrable flows on the complex projective plane CPn.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Language: | English |
| Date: | 2002 |
| Deposited On: | 29 Nov 2010 16:27 |
| Last Modified: | 29 Jul 2020 19:43 |
| Publisher: | Universidad de la Frontera, Chile |
| ISSN: | 0716-7776 |
| OA Status: | Closed |
Topalov, P