## 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 G_{k}(V) is defined as the set of all subspaces W ⊂ V such that
dim(W) = k. In the case of V = R^{n}, G_{k}(V) is the set of k-fl
ats in R^{n} 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.

**Download:** **PDF**

### Submission history

[v1] 16 Aug 2010

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