Differentiable Structures on Real Grassmannians

Authors: Jeidsan A. C. Pereira

Given a vector space V of dimension n and a natural number k < n, the grassmannian Gk(V) is defined as the set of all subspaces W ⊂ V such that dim(W) = k. In the case of V = Rn, Gk(V) is the set of k-fl ats in Rn and is called real grassmannian [1]. Recently the study of these manifolds has found applicability in several areas of mathematics, especially in Modern Differential Geometry and Algebraic Geometry. This work will build two differential structures on the real grassmannian, one of which is obtained as a quotient space of a Lie group [1], [3], [2], [7]

Comments: 10 Pages.

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Submission history

[v1] 16 Aug 2010

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