The Geometry and Topology on Grassmann Manifolds

Abstract

This paper shows that the Grassmann Manifolds $G_{\mathbf{F}}(n,N)$ can all be imbedded in an Euclidean space $M_{\mathbf{F}}(N)$ naturally and the imbedding can be realized by the eigenfunctions of Laplacian $△$ on $G_{\mathbf{F}}(n,N)$. They are all minimal submanifolds in some spheres of $M_{\mathbf{F}}(N)$ 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.

15 pages

Cited by in corpus (1)

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