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Results tagged with smooth-manifolds
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user 7311
Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].
2
votes
Does a *topological* manifold have an exhaustion by compact submanifolds with boundary?
Doesn't this depend on the definition of "manifold". If the only condition is being locally Euclidean, then there are connected non second countable examples (e.g., the "long line") for which the answ …
- 15.3k
12
votes
Accepted
Definition of Sobolev spaces as a space of sections of certain type
There is a fairly careful discussion of this in my book "Foundations of Global Non=Linear Analysis", Benjamin & Co. 1968
(Added later:) It occurred to me that this old book of mine is probably not ea …
- 15.3k
12
votes
Characterization of the Lie derivative
The Lie derivative $L_X$ with respect to a smooth vector field $X$
is of course well-defined on the whole tensor algebra and it is a
derivation of this algebra. If $f$ is a smooth function it satisfi …
- 15.3k