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location India
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visits member for 2 years, 8 months
seen Nov 13 at 14:17

Grad Student with an interest in Riemannian Geometry


Nov
11
comment Diffeomorphism between the Grassmannian manifolds $\mathbf{Gr}(n,k)$ and $\mathbf{Gr}(n,n-k)$.
Should have said this yesterday. Is the map you asked for just obtained by shifting the last $(n-k)$ vectors in $A$ to the first $n-k$ vectors and then listing the remaining $k$ vectors?
Nov
10
accepted Diffeomorphism between the Grassmannian manifolds $\mathbf{Gr}(n,k)$ and $\mathbf{Gr}(n,n-k)$.
Nov
10
comment Diffeomorphism between the Grassmannian manifolds $\mathbf{Gr}(n,k)$ and $\mathbf{Gr}(n,n-k)$.
Thanks a lot for your effort. That is very comprehensive!!!
Nov
10
comment Diffeomorphism between the Grassmannian manifolds $\mathbf{Gr}(n,k)$ and $\mathbf{Gr}(n,n-k)$.
@Thanks for your response. Nope. I am not able to explicitly reason this out. I do vaguely understand what you are trying to teach me. But I am still lost mostly. Is $\alpha$ a sort of projection map? and did you mean $E = <v_1,...,v_k>$??
Nov
10
comment Diffeomorphism between the Grassmannian manifolds $\mathbf{Gr}(n,k)$ and $\mathbf{Gr}(n,n-k)$.
I was working with the Grassmannian as a homogeneous space obtained by the group action of orthogonal group, actually I need to prove that too.
Nov
10
asked Diffeomorphism between the Grassmannian manifolds $\mathbf{Gr}(n,k)$ and $\mathbf{Gr}(n,n-k)$.
Nov
4
comment Help with terminology
Thanks. I had given up hope on this one. But can you point me to a specific chapter where this is discussed.
Nov
4
comment Geometric intuition for the Weingarten map
It is the tangent space to the surface $M$ at the point $x$, in other words, space of tangent vectors to $M$ at $x$.
Oct
25
comment $ \lim_{n\rightarrow \infty}n^{-\frac{1}{2}\left(1+\frac{1}{n}\right)}\cdot \left(1^1\cdot 2^2…n^n\right)^{\frac{1}{n^2}}$
Maybe you can still use product of limits although your first limit is wrong. Its simple enough. The second limit in the product can be obtained by using the "sandwich" theorem. Just look at how the term $(1.2^2.3^2 \ldots n^n)^{\frac{1}{n^2}}$ is bounded.
Oct
25
revised Fixed field of two subgroups of $\operatorname{Aut}_{K}{K(x)}$
improved formatting
Oct
25
suggested suggested edit on Fixed field of two subgroups of $\operatorname{Aut}_{K}{K(x)}$
Oct
24
accepted Clarification of notion of proper group action.
Oct
24
comment Clarification of notion of proper group action.
Gosh!! I was just suggested the same book by a friend. Thanks a lot. Just one clarification. Why the big fuss about moving compact sets and not any other kind??Does bringing in compactness facilitate anything??Thanks again!!
Oct
23
asked Clarification of notion of proper group action.
Oct
22
comment Linear Algebra Subspace question
As Matt said, you seem to have confused the vectors with the components $b_1, b_2, b_3$. All you need to do is just go through the terms and definitions governing this problem, you will be done. I suggest you try and do it yourself.
Oct
16
comment Help with terminology
Should I edit my question in some way?
Oct
16
comment Help with terminology
I have done a first course in Differential Geometry and I am familiar with manifolds, submersions and immersions, but not much of group actions on manifolds or even Grassmannians
Oct
16
asked Help with terminology
Sep
30
awarded  Explainer
Sep
24
awarded  Autobiographer