We describe for any Riemannian manifold M a certain scheme M L, lying in between the first and second neighbourhood of the diagonal of M. Semi-conformal maps between Riemannian manifolds are then analyzed as those maps that preserve M L; harmonic maps are analyzed as those that preserve the (Levi-Civita-) mirror image formation inside M L.
@article{bwmeta1.element.doi-10_2478_BF02475972,
author = {Anders Kock},
title = {A geometric theory of harmonic and semi-conformal maps},
journal = {Open Mathematics},
volume = {2},
year = {2004},
pages = {708-724},
zbl = {1146.51012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475972}
}
Anders Kock. A geometric theory of harmonic and semi-conformal maps. Open Mathematics, Tome 2 (2004) pp. 708-724. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475972/
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