Harmonic homogeneous manifolds of nonpositive curvature

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dc.creatorNikolayevsky, Y.
dc.date2004-07-02
dc.date.accessioned2026-07-07T05:09:54Z
dc.date.available2026-07-07T05:09:54Z
dc.descriptionA Riemannian manifold is called harmonic if its volume density function expressed in polar coordinates centered at any point is radial. Flat and rank-one symmetric spaces are harmonic. The converse (the Lichnerowicz Conjecture) is true for manifolds of nonnegative scalar curvature and for some other classes of manifolds, but is not true in general: there exists a family of homogeneous harmonic spaces, the Damek-Ricci spaces, containing noncompact rank-one symmetric spaces, as well as infinitely many nonsymmetric examples. We prove that a harmonic homogeneous manifold of nonpositive curvature is either flat, or is isometric to a Damek-Ricci space.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/math/0407024
dc.identifierhttp://arxiv.org/abs/math/0407024
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71756
dc.subjectDifferential Geometry
dc.subject53C30; 53C25
dc.titleHarmonic homogeneous manifolds of nonpositive curvature
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