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Results tagged with dg.differential-geometry
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user 33510
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
14
votes
1
answer
677
views
If an equivariant map is smooth on diagonal matrices, is it smooth everywhere?
This is a followup from a question I asked on math.SE, which received a helpful answer but unfortunately not a complete one. $\def\Sym{\mathrm{Sym}_{n\times n}}$
$\def\s{\mathrm{Sym}}\def\sp{\s^+}$Let …
5
votes
0
answers
593
views
Is torsion of a connection always an obstruction to some kind of integrability? [closed]
Let $E$ be a vector bundle over a smooth manifold $M$ equipped with a linear connection $\nabla : \Gamma(E) \to \Omega^1(M;E).$ I say $(M,E,\nabla)$ is flat if it admits trivial local models; i.e. if …
5
votes
Is higher order mean curvature extrinsic or intrinsic
If we let $S: TM \to TM$ denote the shape operator of a hypersurface $M \to \mathbb R^{n+1}$ and $\mathfrak R:\Lambda^2TM\to\Lambda^2TM$ the curvature operator, then the Gauss equation can be written …