[OS X TeX] Intrinsic tensors
Michael Sharpe
msharpe at ucsd.edu
Sat May 31 02:27:46 EDT 2014
On May 30, 2014, at 1:21 PM, Alain Schremmer <schremmer.alain at gmail.com> wrote:
> You are of course quite right but there was a story behind that: Many, many years ago, I had written a piece to introduce the conservations laws of fluid mechanics in a way I thought would be "more elegant". The other day, I looked for it to give to one of my grandsons who is trying to get into nano-technology without really knowing the first word about, say, Navier-Stokes.
>
> Looking at it after all this time, I thought the stuff was not bad so I thought to see how it might go in LaTeX. I have attached the (only) page I did to give you an idea of the way I had gone about it. I still think it has merits. Maybe I will keep LaTexing it. In any case, I wanted to keep the "flavor".
>
> Best regards as always
> --s
>
> On May 30, 2014, at 2:47 PM, Claus Gerhardt wrote:
>
>> Alain,
>>
>> In the literature generic tensors are usually denoted by elements of the Latin or Greek alphabet like T=(T_{\al\bet}) or \eta=(\eta^i), etc. Tensor bundles with base space M are usually denoted by T^{p,q}(M); its elements are tensors of order p+q, where p is the order with respect to the contravariant indices and q with respect to the covariant indices. I wouldn't bother creating fancy symbols but rather adopt the norm.
>>
>> Claus
>>
>>
>> On May 29, 2014, at 19:45, Alain Schremmer <schremmer.alain at gmail.com> wrote:
>>
>>> I would like a symbol to represent n-dimensional objects, in fact tensor fields of order n, something like<G^n.pdf>.
>>>
>>> I have looked around to no avail; worse comes to worst, I can always use the above pdf but I am curious.
>>>
>>> Faintly hopeful regards
>>> --schremmer
>>>
>>>
Alain's query raises a point I think is very important. Those of us now in our advanced years were educated when it was not always easy to disseminate work which was incomplete or excursive, however original. Documents, sometimes handwritten, sometimes typed in pseudo-math mode, survive in some cases in the form of "lecture notes" that are highly valued by experts, copied only to their students, and therefore at risk of being lost to future generations of mathematicians outside the mainstream. I think those of our generation should do what they can to preserve those lecture notes by publishing them as pdf web documents with added commentaries and links to later relevant work so that mathematical history may benefit from our soon-to-be extinct knowledge. In most cases, this will require a scan of the original plus annotations.
Michael
.
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