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Of late, I've seen more work on the sub-Riemannian geometry of the Heisenberg group than on the Riemannian geometry. Two good texts on this topic are: An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem by Capogna, Danielli, Pauls, Tyson Birkhauser, 2007 Geometric Analysis on the Heisenberg Group and Its Generalizations by Calin, Chang, Greiner, AMS/IP, 2007 I don't know if this counts as particularly "hot," but I have found these to be interesting approaches.
This equation is a bit problematic. If $\alpha$ is a $k$-form, then $d\alpha$ is a $(k+1)$-form and $\delta\alpha$ is a $(k-1)$-form. I suppose you could interpret this equation as living on the entire space of forms, i.e., $\alpha$ is of mixed type. Did you mean to solve $(d+\delta)^2\alpha=0$? Those are the harmonic forms.
Thanks, Liviu. Your solution and interest are both gratifying. The problem is even more interesting given the context in which it was given to me -- namely, cellular anticlinal division. This is a case where Nature is doing the optimization for us.
Hi, Liviu, It is an easily solved problem. I was just curious if anyone knew of a published version of the solution in order to give credit where credit is due.
