Timeline for Some notational questions regarding tangent vectors
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 28, 2015 at 20:27 | answer | added | Peter Michor | timeline score: 3 | |
| Oct 28, 2015 at 16:25 | comment | added | Sebastian Goette | I don't have a handy name for the objects in Q1. But they are dual to jets, where an $\ell$-jet is the collection of derivatives up to order $\ell$ of a given $C^\ell$-function on $M$, taken at one point $p$. The set of $\ell$-jets at a point $p\in M$ forms a vector space that is dual to the space you are describing. However, the global structure of the jet bundle is more complicated. So you may try to find something on jets in the literature. | |
| Oct 28, 2015 at 11:49 | history | edited | erz | CC BY-SA 3.0 |
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| Oct 28, 2015 at 11:47 | comment | added | erz | Actually, I have a differential "functional", so to speak, since it acts locally at a point. But If I have a vector field, we can talk about operator. Thank you for bringing up this topic, I'll update the question. | |
| Oct 28, 2015 at 11:21 | comment | added | erz | I was thinking about this, but isn't the term "differential operator" reserved for more specific things, like the ones they consider in mathematical physics? | |
| Oct 28, 2015 at 11:17 | comment | added | Robert Bryant | It seems that what you are searching for is the notion of a differential operator of order at most $l$ on the sections of a vector bundle over $M$. If you don't want to mention $l$ explicitly, you can simply talk about the $C^k$ differential operators. (The usual tangent bundle is defined in terms of the first order differential operators.) | |
| Oct 28, 2015 at 10:48 | history | asked | erz | CC BY-SA 3.0 |