Geometry

   

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.

Download: PDF

Submission history

[v1] 16 Aug 2010

Unique-IP document downloads: 656 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus