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I'm wondering is there any branches of Chemistry that make use of manifolds, Riemann geometry, tensors etc. So far I have not come across anything but hoped that the wider community would know of something?

Forgive me if this is too vague a question but I'm just looking for some topics I can research myself.

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    $\begingroup$ How many chemist you think know differential geometry? So, unless you try to explain what the hell is manifold and all other stuff you mentioned, your question is very unlikely to be answered. $\endgroup$
    – Wildcat
    Commented Sep 21, 2014 at 10:59
  • $\begingroup$ The only thing I could come up by reading the Wikipedia article on manifold, is that potential energy surfaces do have some topological properties, thus, there should be some use of differential geometry for analysis of potential energy surfaces. Then I just googled and found something, say, dx.doi.org/10.1007/978-94-009-2313-3_3 amongst many other papers. $\endgroup$
    – Wildcat
    Commented Sep 21, 2014 at 11:06
  • $\begingroup$ The author of the paper linked above also wrote a book with an interesting title "Shape in Chemistry: An Introduction to Molecular Shape and Topology" eu.wiley.com/WileyCDA/WileyTitle/productCd-0471187410.html $\endgroup$
    – Wildcat
    Commented Sep 21, 2014 at 11:10
  • $\begingroup$ Aha, there is the so-called chemical topology. There is even a short article in Wiki about it (en.wikipedia.org/wiki/Topology_%28chemistry%29) and some books with exactly this title (crcpress.com/product/isbn/9789056991746). $\endgroup$
    – Wildcat
    Commented Sep 21, 2014 at 11:15
  • $\begingroup$ And I hope, the information above is relevant, since I have no idea what these papers and books are about. :D $\endgroup$
    – Wildcat
    Commented Sep 21, 2014 at 11:16

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  • We use tensors in my research lab to analyze solid state NMR.

  • In my research laboratory we use manifolds all the time for stimulating annealing calculations.

There are several research groups in physical chemistry which utilize what you are describing, but it will never be an undergraduate topic. One particular group that comes to mind that uses this sort of stuff a lot is the Hirata group at the University of Illinois. They actually made a piece of software called the Tensor Contraction Engine. http://www.scs.illinois.edu/~sohirata/software.html

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  • $\begingroup$ Also tensors in EPR and solution state paramagnetic NMR $\endgroup$
    – DavePhD
    Commented Nov 10, 2015 at 13:39

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