Invariant totally geodesic unit vector fields on three-dimensional Lie groups

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dc.creatorYampolsky, Alexander
dc.date2005-12-20
dc.date.accessioned2026-07-07T06:55:35Z
dc.date.available2026-07-07T06:55:35Z
dc.descriptionWe give a complete list of those left invariant unit vector fields on three-dimensional Lie groups with the left-invariant metric that generate a totally geodesic submanifold in the unit tangent bundle of a group with the Sasaki metric. As a result, each class of three-dimensional Lie groups admits the totally geodesic unit vector field. From geometrical viewpoint, the field is either parallel or characteristic vector field of a natural almost contact structure on the group.
dc.description38 pages
dc.identifierhttps://arxiv.org/abs/math/0512478
dc.identifierhttp://arxiv.org/abs/math/0512478
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106327
dc.subjectDifferential Geometry
dc.subjectGroup Theory
dc.subject53B20, 53B25
dc.titleInvariant totally geodesic unit vector fields on three-dimensional Lie groups
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