Timeline for Angle between two vectors in a Minkowski (Finsler) space
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Mar 19, 2022 at 17:24 | history | edited | YCor | CC BY-SA 4.0 |
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| Dec 23, 2017 at 17:30 | comment | added | Majid | @AntonPetrunin Is there any reference that I can refer to? | |
| Dec 23, 2017 at 17:29 | comment | added | Majid | @AntonPetrunin what do you mean by the most important property of angle and use it as the definition? The only thing that I know is that the angle is the cos^-1 or sin^-1 of the inner product or exterior product divided by the norms! | |
| Dec 20, 2017 at 22:11 | comment | added | Majid | @AntonPetrunin if you are talking about my case, no. If you are talking about some definition of angle, I do not know. My problem is that I saw through some examples that the angle between two special vector fields is constant along a submanifold. I am suspected that it is true is general case of my problem and so I needed to define the angle. | |
| Dec 20, 2017 at 20:15 | comment | added | Anton Petrunin | @Majid, is not it the first variation formula if you move in the direction $v$ and measure the distances to a point in the direction $w$? | |
| Dec 20, 2017 at 19:43 | comment | added | user44143 | I agree with @AntonPetrunin. Following Busemann, I would also say: do you need vectors? Perhaps define the angle at $p$ between curves $a$ and $b$ as $2 \lim \arcsin d(a_s, b_s)/2s$, where $a_s$ and $b_s$ are the points at distance $s$ from $p$ along the curves. | |
| Dec 20, 2017 at 19:39 | comment | added | Majid | @AntonPetrunin You mentioned that different properties lead to different definitions. Is there any property which leads to my second definition? | |
| Dec 20, 2017 at 19:38 | comment | added | Majid | @AntonPetrunin I need the angle in the case of Finsler since I am trying to show that the angle between two special vectors remain constant along a submanifold. Could you please give me some reference where the angle in Riamannian is defined. You mentioned that the one that I defined looks OK. Which one? I have defined two. | |
| Dec 20, 2017 at 18:57 | comment | added | Anton Petrunin | I doubt that you need angle in Finsler space. If you insist, then look at Riemannian case, choose the most important property of angle and use it as the definition --- typically different properties lead to different definitions. The one you propose looks okey, it is not symmetric, but you always have to sacrifice something in the Finsler world. | |
| Dec 20, 2017 at 17:24 | history | asked | Majid | CC BY-SA 3.0 |