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A geometric theory of harmonic and semi-conformal maps. (English) Zbl 1146.51012
This paper has some overlap with the author’s [Theory Appl. Categ. 9, 1–16, electronic only (2001; Zbl 1026.18007)].
The author, using a subscheme $$M_{L}\subseteq M\times M$$ between the first and second neighborhood of the diagonal of any Riemannian manifold $$M$$, characterizes semi-conformal maps and harmonic maps geometrically. The present paper is more refined in the construction of $$M_{L}$$ and the proofs than the preceding paper. The new results in the present paper are the characterization of semi-conformality and a version of the theorem of B. Fuglede [Ann. Inst. Fourier 28, No. 2, 107–144 (1978; Zbl 0339.53026)] and T. Ishihara [J. Math. Kyoto Univ. 19, 215–229 (1979; Zbl 0421.31006)] talking about harmonic $$2$$-jets in place of harmonic germs. The latter is almost immediate from the geometric descriptions of harmonic and semi-conformal maps.

##### MSC:
 51K10 Synthetic differential geometry
Full Text:
##### References:
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