The Geometry and Topology on Grassmann Manifolds

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dc.creatorZhou, Jianwei
dc.date2006-08-03
dc.date.accessioned2026-07-07T07:21:19Z
dc.date.available2026-07-07T07:21:19Z
dc.descriptionThis paper shows that the Grassmann Manifolds $G_{\bf F}(n,N)$ can all be imbedded in an Euclidean space $M_{\bf F}(N)$ naturally and the imbedding can be realized by the eigenfunctions of Laplacian $\triangle$ on $G_{\bf F}(n,N)$. They are all minimal submanifolds in some spheres of $M_{\bf F}(N)$ respectively. Using these imbeddings, we construct some degenerate Morse functions on Grassmann Manifolds, show that the homology of the complex and quaternion Grassmann Manifolds can be computed easily.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/math/0608073
dc.identifierhttp://arxiv.org/abs/math/0608073
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115263
dc.subjectDifferential Geometry
dc.subject14M15,53C42,57R70
dc.titleThe Geometry and Topology on Grassmann Manifolds
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