On extrinsic geometry of unit normal vector fields of Riemannian hyperfoliations

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dc.creatorYampolsky, Alexander
dc.date2005-03-24
dc.date2005-05-10
dc.date.accessioned2026-07-07T05:18:25Z
dc.date.available2026-07-07T05:18:25Z
dc.descriptionWe consider a unit normal vector field of (local) hyperfoliation on a given Riemannian manifold as a submanifold in the unit tangent bundle with Sasaki metric. We give an explicit expression of the second fundamental form for this submanifold and a rather simple condition its totally geodesic property in the case of a totally umbilic hyperfoliation. A corresponding example shows the non-triviality of this condition. In the 2-dimensional case, we give a complete description of Riemannian manifolds admitting a geodesic unit vector field with totally geodesic property.
dc.description13 pages
dc.identifierhttps://arxiv.org/abs/math/0503566
dc.identifierhttp://arxiv.org/abs/math/0503566
dc.identifierPubl. Math. Debrecen 63/4 (2003), 565 -- 567
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74654
dc.subjectDifferential Geometry
dc.subject53B25, 53C25
dc.titleOn extrinsic geometry of unit normal vector fields of Riemannian hyperfoliations
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