matgaio

Rio de Janeiro, Brazil

Aug
26
asked Geodesics of Sasaki metric
Aug
18
asked Normal fields of geodesic spheres
Aug
5
comment Normal curvature of geodesic spheres
Dear @NormalHuman, this is a nice example, thank you. I can't see if it is possible for this example to be the universal covering of a compact Riemannian manifold. If it is not, perhaps I can have some hope. I'm interested in investigate this Lipschitz constant in universal coverings of compact Riemannian manifolds without conjugate points.
Aug
4
comment Normal curvature of geodesic spheres
Hi, @AntonPetrunin, indeed. Allow me to go a little further on my question. I see that if I fix the radius $R$, the normal vector is Lipschitz as you pointed out, and it appears to me that the Lipschitz constant $L$ will depend on $R$. Letting the radius $R>1$ be arbitrary large (in the abscense of conjugate points), do you have any feeling on if it is possible to have some upper bound for the Lipschitz constants?
Aug
4
comment Normal Variation on Manifolds
Dear @AntonPetrunin, I'm interested in this sort of questions too. In particular, I've asked (math.stackexchange.com/questions/1383511/…) a related question in abscense of conjugate points. Would you mind giving me some references? Thanks a lot!
Aug
3
revised Normal curvature of geodesic spheres
edited tags
Aug
3
asked Normal curvature of geodesic spheres
Mar
22
awarded Yearling
Mar
22
awarded Yearling
Feb
24
comment a.e.-defined integrable functions on $X$.
I think the answer is the following: let us denote the domain of the function $f$ by $D(f)\subset X$. The expression "a.e.-defined integrable functions on $X$" means that $\mu\big(X-D(f)\big)=0$ and $f$ is integrable in $D(f)$
Feb
13
asked Landsberg angle
Jan
18
comment Bi-asymptotic geodesics in Visibility manifolds
Thanks again. Our conversations on the subject have opened my eyes for several points on this theory.
Jan
18
accepted Bi-asymptotic geodesics in Visibility manifolds
Jan
13
comment Bi-asymptotic geodesics in Visibility manifolds
I see. It doesn't help. I can consider just $\mathbb{H}^2\times\mathbb{R}$.
Jan
13
comment Bi-asymptotic geodesics in Visibility manifolds
I have in addition the abscense of conjugate points, if it helps...
Jan
13
revised Bi-asymptotic geodesics in Visibility manifolds
added 40 characters in body
Jan
13
comment Bi-asymptotic geodesics in Visibility manifolds
Yes, you are completely right. I have wrote (and after I deleted it) the non-compact condition, but I thought it was perhaps unnecessary to comment. I will put this there to make more sense to the question. Thanks again!
Jan
13
asked Bi-asymptotic geodesics in Visibility manifolds
Oct
29
awarded Supporter
Oct
8
awarded Tumbleweed
1 2 3 4 5