Timeline for How to prove that a subset in a vector space is an indicatrix?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 29, 2017 at 17:25 | vote | accept | Majid | ||
| Jun 29, 2017 at 17:24 | vote | accept | Majid | ||
| Jun 29, 2017 at 17:25 | |||||
| Jun 29, 2017 at 17:23 | vote | accept | Majid | ||
| Jun 29, 2017 at 17:24 | |||||
| Jun 28, 2017 at 9:04 | comment | added | alvarezpaiva | That would be like calling every tangent vector a parametrization because you can write it as the derivative at time zero of some smooth curve. It was meant to be the hessian of the norm at a nonzero point, but we screwed up writing it and didn't notice until now. Thanks. | |
| Jun 27, 2017 at 23:44 | comment | added | Majid | I thought that you used this parametrization to show that $g_{\varphi}(\pi(v))$ is an inner product. | |
| Jun 27, 2017 at 5:46 | comment | added | alvarezpaiva | What parametrization? At every one of its points a smooth quadratically convex body has an oscullating ellipsoid. There is nothing more there. Proposition 2.1 is just the analytic representation of the quotient norm (it holds even when the convex body is not quadratically convex) and Proposition 2.2 is the rather simple statement that when you project a quadratically convex body, then the osculating ellipsoids at the singular points of the projection project themselves to the osculating ellipsoids of the projected body. | |
| Jun 26, 2017 at 22:01 | comment | added | Majid | You mean I can still use Propositions 2.1 and 2.2? Where did you use such a parameterization then? | |
| Jun 26, 2017 at 19:13 | comment | added | alvarezpaiva | Gee, you are right. It's wrong. I don't know what I (or we) were thinking, but it was just meant to be the Hessian in an affine space ( and so its well defined, if you don't mess up like we did). | |
| Jun 26, 2017 at 19:02 | comment | added | alvarezpaiva | It's supposed to just be the hessian of $\varphi^2$ in the affine space $V$ evaluated at the point $v$. Let me check what we wrote. | |
| Jun 26, 2017 at 13:37 | comment | added | Majid | Trying to understand your paper, I have difficulties and some doubts about the parameterization that you are suggesting before Definition 2.2. I mean the vector-valued function $\alpha$. Suppose that $V=R^3$ and the Minkowski norm $F$ is the canonical metric, i.e. $F=||.||$. Define $\alpha: R^2\mapsto S$, where $S$ is the unit sphere, as $\alpha(x,y)=(x,y,\sqrt{1-x^2-y^2})$. Then $F^2(\alpha)=1$ and so each partial derivative of it is zero. In particular $g_{\varphi}(0,0,1)=0$. I am wondering the definition provided for the fundamental tensor is well-defined? | |
| Jun 20, 2017 at 20:29 | comment | added | alvarezpaiva | Propositions 2.1 and 2.2. Yes, it's just que quotient norm. | |
| Jun 20, 2017 at 18:22 | comment | added | Majid | the quotient norm on $V_2$ is $F_2$ then? | |
| Jun 20, 2017 at 18:18 | comment | added | Majid | Thanks a lot for your answer. I am reading exactly this paper and this is why I asked this question here. Which pert of the paper is mentioning this construction? | |
| Jun 20, 2017 at 18:08 | history | answered | alvarezpaiva | CC BY-SA 3.0 |