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The Geometry and Topology on Grassmann Manifolds

Authors
  • Zhou, Jianwei
Type
Preprint
Publication Date
Aug 02, 2006
Submission Date
Aug 02, 2006
Identifiers
arXiv ID: math/0608073
Source
arXiv
License
Unknown
External links

Abstract

This 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.

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