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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].

1 vote
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80 views

Can this problem be rephrased as optimization on a manifold?

I have question. I have a Riemmanian manifold $\mathcal{M}$, like an $n$-dimensional regular surface in $\mathbb{R}^n$. And I have a smooth scalar field defined on this manifold $f:\mathcal{M} \to \ma …
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1 vote
0 answers
199 views

Fourier transform of functions mapping manifolds, is there a definition?

$\DeclareMathOperator\SO{SO}$I have a problem which boils down to the analysis of functions of the form $$ f : \mathbb{R} \to \SO(3)^n $$ Since $\SO(3)$ is a compact group so is $\SO(3)^n$. Now if ins …
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