All Questions
Tagged with hilbert-spaces riemannian-geometry
7 questions
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Quotients of the Hilbert space
Let $G$ be a compact Lie group with a biinvariant metric.
Note that $G\times G$ acts isometrically on $G$ from left and right.
Consider the quotient $D=G/H$ by a closed subgroup $H\le G\times G$;
if $...
- 45k
2
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0
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120
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Closure of Laplacian
Let $(M,g)$ be a complete Riemannian manifold and $\Delta$ the (positive) Laplace-Beltrami operator. Now, consider this operator as an operator
$$\Delta:\mathcal{D}(\Delta)\to L^{2}(M)$$
There are two ...
- 1,171
8
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Is there any physics theory which is similar to these analogies?
Since I am doing this little "research" project on my spare time and in my physical neighborhood there are not many people to discuss these ideas, I wanted to share with you a small point of ...
- 3,064
2
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1
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267
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volume of parallelotope in $L^2(\mathbb R).$ [closed]
Let $L^2(\mathbb R)$ is complex Hilbert space with standard inner product.
Does it make sense to talk of volume of parallelotope formed by following vectors in $L^2(\mathbb R):$ say, e.g.,
$$\{ f(...
- 305
2
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210
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A Riemannian metric on the plane such that the intersection of every two discs is a disc, again
Is there a Riemannian metric on $\mathbb{R}^2$ (or a $2$ dimensional manifold) such that the intersection of every two open discs is an open disc, again?
As linear version of this question we ask:
...
- 356
1
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1
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94
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Embedding Riemmanian Manifold Linearly
Given a Hilbert Manifold $M$ does there exist a smooth map into some very large Hilbert space taking geodesics to straight lines?
- 5,405
2
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Equivariant exponential map on Hilbert manifolds
Let $M$ be a Hilbert Riemannian manifold and $G$ a finite-dimensional Lie group acting on $M$. It is well-known that when $M$, too, is finite-dimensional
$$\exp_p: U \subset T_pM \rightarrow \exp_p(U) ...
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