Geodesics on Lie groups: Euler equations and totally geodesic subgroup

dc.contributor.authorModin, K.
dc.contributor.authorPerlmutter, M.
dc.contributor.authorMarsland, S.
dc.contributor.authorMcLachlan, R.
dc.date.accessioned2013-05-22T02:44:50Z
dc.date.available2013-05-22T02:44:50Z
dc.date.issued2010
dc.description.abstractThe geodesic motion on a Lie group equipped with a left or right invariant Riemannian metric is governed by the Euler-Arnold equation. This paper investigates conditions on the metric in order for a given subgroup to be totally geodesic. Results on the construction and characterisation of such metrics are given. The setting works both in the classical nite dimensional case, and in the category of in nite dimensional Fr echet Lie groups, in which di eomorphism groups are included. Using the framework we give new examples of both nite and in nite dimensional totally geodesic subgroups. In particular, based on the cross helicity, we construct right invariant metrics such that a given subgroup of exact volume preserving di eomorphisms is totally geodesic. The paper also gives a general framework for the representation of Euler-Arnold equations in arbitrary choice of dual pairing.en
dc.identifier.citationModin, K., Perlmutter, M., Marsland, S., McLachlan, R. (2010), Geodesics on Lie groups: Euler equations and totally geodesic subgroups, Research Letters in the Information and Mathematical Sciences, 14, 79-106en
dc.identifier.issn1175-2777
dc.identifier.urihttp://hdl.handle.net/10179/4512
dc.language.isoenen
dc.publisherMassey Universityen
dc.subjectEuler equationsen
dc.subjectTotally geodesic subgroupsen
dc.subjectDi eomorphism groupsen
dc.subjectLie groupsen
dc.titleGeodesics on Lie groups: Euler equations and totally geodesic subgroupen
dc.typeArticleen
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