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Results tagged with dg.differential-geometry
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user 49740
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
7
votes
2
answers
508
views
When distance nonincreasing map is an isometry
Let $f: M \to M$ be a distance nonincreasing map between a closed Riemannian manifold $M$
and $f$ is homotopic to the idendity map. Is it then $f$ an isometry?
- 157
3
votes
2
answers
358
views
lift of Riemannian metric to branched double cover
Let $\hat{M}$ be a branched double cover of $M$. Is there a way to lift a Riemannian metric $g$ on $M$ to get a smooth Riemannian metric $\hat{g}$ on $\hat{M}$. Moreover, if $g$ has nonnegative secti …
- 157
0
votes
1
answer
185
views
extension of Riemannian metric on real affine variety
Given a Riemannian metric $g$ on the real part $X_R$ of a real affine variety $X$,
is there a "natural" way to extend $g$ to be a Riemannian metric on $X$?
- 157
4
votes
0
answers
166
views
Riemannian metric on complexification of Lie group
Let $G$ be a compact linear group and $G^c$ be its complexification. Then there is a diffeomorphism $f: G^c \to G \times Lie(G) $ given by $$ x e^{iA} \to (x,A).$$
Let $h$ be the pull back metric of …
- 157