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Geodesically compatible metrics. Existence of commutative conservation laws


Topalov, P (2002). Geodesically compatible metrics. Existence of commutative conservation laws. Cubo Matemática Educacional, 4(2):371-399.

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. We apply our results for obtaining an infinite family (hierarchy) of completely integrable flows on the complex projective plane CPn.

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. We apply our results for obtaining an infinite family (hierarchy) of completely integrable flows on the complex projective plane CPn.

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Additional indexing

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:05 Apr 2016 13:25
Publisher:Universidad de la Frontera, Chile
ISSN:0716-7776

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