I need to study Grassmannian manifold in a good way, like study vector bundles, tangent bundle,... and etc on Grassmannian manifold. I found some lecture and books but they were written an inappropriate way, I mean, they just mentioned the definition and some theorems related to Grassmannian.

Does anybody know any nice reference?

Thank you in advance.



You might take a look at Milnor-Stasheff's "Characteristic Classes", chapter 5. In the first three chapters they introduce some basic concepts about Manifolds and Vector bundles. Chapter 5 deals with the Grassmanians. In my opinion it is a good starting point.


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