Mixing
Several Questions about Hilbert Manifold
1
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These should be quite fundamental questions about the definitions about Hilbert manifold yet I cannot find answers about them after a long-time search:
- How is the tangent space at a point on a Hilbert manifold defined?
- What does it mean by a map between two Hilbert manifold being $C^k$ (I am particularly interested in $C^infty$)?
- How is the differential of a map between two Hilbert manifold defined?
Thank you for helping me out!
manifolds hilbert-spaces riemannian-geometry
asked Jan 22 at 4:42
JerryJerry
457313
$endgroup$
add a comment |
1
$begingroup$
These should be quite fundamental questions about the definitions about Hilbert manifold yet I cannot find answers about them after a long-time search:
- How is the tangent space at a point on a Hilbert manifold defined?
- What does it mean by a map between two Hilbert manifold being $C^k$ (I am particularly interested in $C^infty$)?
- How is the differential of a map between two Hilbert manifold defined?
Thank you for helping me out!
manifolds hilbert-spaces riemannian-geometry
asked Jan 22 at 4:42
JerryJerry
457313
$endgroup$
1
$begingroup$
The easiest answer for all three is "in charts". Lang's book "differentiable manifolds" covers the Banach manifold case.
$endgroup$
– user98602
Jan 22 at 6:26
add a comment |
1
1
1
$begingroup$
These should be quite fundamental questions about the definitions about Hilbert manifold yet I cannot find answers about them after a long-time search:
- How is the tangent space at a point on a Hilbert manifold defined?
- What does it mean by a map between two Hilbert manifold being $C^k$ (I am particularly interested in $C^infty$)?
- How is the differential of a map between two Hilbert manifold defined?
Thank you for helping me out!
manifolds hilbert-spaces riemannian-geometry
asked Jan 22 at 4:42
JerryJerry
457313
$endgroup$
These should be quite fundamental questions about the definitions about Hilbert manifold yet I cannot find answers about them after a long-time search:
- How is the tangent space at a point on a Hilbert manifold defined?
- What does it mean by a map between two Hilbert manifold being $C^k$ (I am particularly interested in $C^infty$)?
- How is the differential of a map between two Hilbert manifold defined?
Thank you for helping me out!
manifolds hilbert-spaces riemannian-geometry
manifolds hilbert-spaces riemannian-geometry
asked Jan 22 at 4:42
JerryJerry
457313
asked Jan 22 at 4:42
JerryJerry
457313
asked Jan 22 at 4:42
JerryJerry
457313
asked Jan 22 at 4:42
JerryJerry
457313
asked Jan 22 at 4:42
JerryJerry
457313
457313
1
$begingroup$
The easiest answer for all three is "in charts". Lang's book "differentiable manifolds" covers the Banach manifold case.
$endgroup$
– user98602
Jan 22 at 6:26
add a comment |
1
$begingroup$
The easiest answer for all three is "in charts". Lang's book "differentiable manifolds" covers the Banach manifold case.
$endgroup$
– user98602
Jan 22 at 6:26
1
1
$begingroup$
The easiest answer for all three is "in charts". Lang's book "differentiable manifolds" covers the Banach manifold case.
$endgroup$
– user98602
Jan 22 at 6:26
$begingroup$
The easiest answer for all three is "in charts". Lang's book "differentiable manifolds" covers the Banach manifold case.
$endgroup$
– user98602
Jan 22 at 6:26
add a comment |
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1
$begingroup$
The easiest answer for all three is "in charts". Lang's book "differentiable manifolds" covers the Banach manifold case.
$endgroup$
– user98602
Jan 22 at 6:26