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Results tagged with geodesics
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user 46290
0
votes
Nearly length minimizing paths are close to geodesics?
$\newcommand{\Im}{\operatorname{Image}}$
I am trying to construct a complete argument based on Pietro's suggestion:
I assume $M$ is complete.
Assume by contradiction the claim is false. Then there …
- 6,741
3
votes
1
answer
209
views
Nearly length minimizing paths are close to geodesics? [closed]
It's known that length minimizing curves are geodesics (after a possible reparametrization).
Now fix* points $p,q \in M$
Is the following assertion true? …
- 6,741
4
votes
1
answer
432
views
Smooth manifolds for which every metric is geodesically convex
Are there non compact smooth manifolds which have the property that every Riemannian metric is geodesically convex?
Note that a manifold for which every Riemannian metric is complete must be compact. …
- 6,741
6
votes
1
answer
792
views
Totally geodesic subgroups in Lie groups
Since $g$ is bi-$H$-invariant, the geodesics of $H$ are the one-parameter subgroups of $H$. Hence, the question amounts to:
Are the one-parameter subgroups of $H$ geodesics in $G$? …
- 6,741
2
votes
1
answer
232
views
If any two triangles of equal area can be mapped via affine maps, what can we say about the ...
(equivalently, $f$ maps parametrized geodesics to parametrized geodesics.
Here $\nabla=\nabla^{T^*M} \otimes \nabla^{f^*TM}$). …
- 6,741