Energy of Radial Vector Fields on Compact Rank One Symmetric Spaces |
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Authors: | Boeckx E Gonzlez-Dvila J C Vanhecke L |
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Institution: | (1) Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium;(2) Departamento de Matemática Fundamental, Sección de Geometría y Topología, Universidad de La Laguna, La Laguna, Spain |
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Abstract: | We consider the energy (or the total bending) of unit vector fields oncompact Riemannian manifolds for which the set of its singularitiesconsists of a finite number of isolated points and a finite number ofpairwise disjoint closed submanifolds. We determine lower bounds for theenergy of such vector fields on general compact Riemannian manifolds andin particular on compact rank one symmetric spaces. For this last classof spaces, we compute explicit expressions for the total bending whenthe unit vector field is the gradient field of the distance function toa point or to special totally geodesic submanifolds (i.e., for radialunit vector fields around this point or these submanifolds). |
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Keywords: | unit vector fields with singularities energy and total bending of a unit vector field harmonic unit vector fields radial unit vector fields on compact rank one symmetric spaces |
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