185 reputation
6
bio website thomas.ricatte.fr
location France
age 27
visits member for 1 year, 10 months
seen Jul 30 at 9:22

"La porte la mieux fermée est celle que l'on peut laisser ouverte" (Lao-Tseu - Tao-Tö-King)


Jun
17
comment How does one denote the set of all positive real numbers?
@YuvalFilmus Do not forget that this is just an english convention. In France for example, we usually say that 0 is both positive and negative. I have often seen $\mathbb{R}^+$ for all positive/null numbers and $\mathbb{R}^{\ast +}$ for all strictly positive numbers.
Mar
31
asked Quadratic minimization with real output
Sep
17
comment Smooth mapping between Manifolds
Thanks for your answer. Using $V$ and $V'$ identification seems indeed to make sense and allows me to explain better why I can transport the structure !
Sep
17
accepted Smooth mapping between Manifolds
Sep
17
comment Smooth mapping between Manifolds
Ok thanks. Yes both spaces are diffeomorphic wrt the usual smooth structure but I wasn't 100% sure that it was enough to pull back the Riemanian metric (I am mainly into computer science and I lack of formalism when it comes to deal with Riemanian geometry)
Sep
17
comment Smooth mapping between Manifolds
$f^{-1}$ is still linear. I have changed bijection into isomorphism to reflect this fact so $g_\mathcal{N}$ is bilinear. I am not sure if I can use $f$ to move the tangent spaces (point 2.). If it is the case, I should be able to pull back the vectors using $f^{-1}$.
Sep
17
comment Smooth mapping between Manifolds
@AnthonyCarapetis I have edited the post following your first comment. Sorry for the lack of clarity.
Sep
17
revised Smooth mapping between Manifolds
added 114 characters in body
Sep
17
revised Smooth mapping between Manifolds
added 58 characters in body
Sep
17
asked Smooth mapping between Manifolds
Aug
7
awarded  Editor
Aug
7
awarded  Scholar
Aug
7
comment Geodesic complete subset of a connected manifold
@DanielRust I have updated the question to reflect this case.
Aug
7
revised Geodesic complete subset of a connected manifold
Updating question
Aug
7
accepted Geodesic complete subset of a connected manifold
Aug
6
awarded  Student
Aug
6
comment Geodesic complete subset of a connected manifold
@DanielRust Yes of course ! I must be tired and missing the most obvious thing. The set of geodesics works in this case. I guess we can find other examples by this idea of getting stuck to a dimension (like any plane $P$ in $\mathbf{R}^3$). This question was really silly actually :)
Aug
6
comment Geodesic complete subset of a connected manifold
@hardmath For me an open convex subset $O$ of the plane $P$ embedded with a simple Euclidean metric is geodesic convex but not complete since for $x,y\in O$, $\gamma(t)=t*x+(1-t)*y$ will escape from $O$. It could be the case with some specific metric but could become unconnected in this case ?
Aug
6
asked Geodesic complete subset of a connected manifold
May
29
awarded  Supporter