Totally geodesic property of the Hopf vector field

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dc.creatorYampolsky, A.
dc.date2005-03-25
dc.date.accessioned2026-07-07T05:18:29Z
dc.date.available2026-07-07T05:18:29Z
dc.descriptionWe prove that the Hopf vector field is a unique one among geodesic covariantly normal unit vector fields on spheres such that the submanifold generated by the field is totally geodesic in the unit tangent bundle with Sasaki metric. As application, we give a new proof of stability (instability) of the Hopf vector field with respect to volume variation using standard approach from the theory of submanifolds and find exact boundaries for the sectional curvature of the Hopf vector field.
dc.identifierhttps://arxiv.org/abs/math/0503594
dc.identifierhttp://arxiv.org/abs/math/0503594
dc.identifierActa Math. Hungar. 101, 1-2 (2003), 73-92
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74675
dc.subjectDifferential Geometry
dc.subject53B25, 53C42
dc.titleTotally geodesic property of the Hopf vector field
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