# A geometric theory of harmonic and semi-conformal maps

Open Mathematics (2004)

- Volume: 2, Issue: 5, page 708-724
- ISSN: 2391-5455

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topAnders Kock. "A geometric theory of harmonic and semi-conformal maps." Open Mathematics 2.5 (2004): 708-724. <http://eudml.org/doc/268808>.

@article{AndersKock2004,

abstract = {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.},

author = {Anders Kock},

journal = {Open Mathematics},

keywords = {51K10; 53A30; 53C43},

language = {eng},

number = {5},

pages = {708-724},

title = {A geometric theory of harmonic and semi-conformal maps},

url = {http://eudml.org/doc/268808},

volume = {2},

year = {2004},

}

TY - JOUR

AU - Anders Kock

TI - A geometric theory of harmonic and semi-conformal maps

JO - Open Mathematics

PY - 2004

VL - 2

IS - 5

SP - 708

EP - 724

AB - 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.

LA - eng

KW - 51K10; 53A30; 53C43

UR - http://eudml.org/doc/268808

ER -

## References

top- [1] P. Baird and J.C. Wood: Harmonic Morphisms Between Riemannian Manifolds, Oxford University Press, 2003. Zbl1055.53049
- [2] E. Dubuc: “C ∞ schemes”, Am. J. Math, Vol. 103, (1981), pp. 683–690. http://dx.doi.org/10.2307/2374046 Zbl0483.58003
- [3] A. Grothendieck: Techniques de construction en géometrie algébrique, Sem. H. Cartan, Paris, 1960–61, pp. 7–17.
- [4] A. Kock: Synthetic Differential Geometry, Cambridge University Press, 1981.
- [5] A. Kock: “A combinatorial theory of connections”, Contemporary Mathematics, Vol. 30, (1984), pp. 132–144.
- [6] A. Kock: “Geometric construction of the Levi-Civita parallelism”, Theory and Applications of Categories, Vol. 4(9), (1998). Zbl0923.51016
- [7] A. Kock: “Infinitesimal aspects of the Laplace operator”, Theory and Applications of Categories Vol. 9(1), (2001). Zbl1026.18007
- [8] A. Kock: “First neighbourhood of the diagonal, and geometric distributions”, Universitatis Iagellonicae Acta Math., Vol. 41. (2003), pp. 307–318. Zbl1073.53020
- [9] A. Kock and R. Lavendhomme: “Strong infinitesimal linearity, with applications to strong difference and affine connections”, Cahiers de Top. et Géom. Diff., Vol. 25, (1984), pp. 311–324. Zbl0564.18009
- [10] A. Kumpera and D. Spencer: “Lie Equations”, Annals of Math. Studies, Vol. 73, Princeton, 1972. Zbl0258.58015
- [11] F.W. Lawvere: “Toward the description in a smooth topos of the dynamically possible motions and deformations of a continuous body”, Cahiers de Top. et Géom. Diff., Vol. 21, (1980), pp. 377–392. Zbl0472.18009
- [12] B. Malgrange: “Equations de Lie”, I, J. Diff. Geom., Vol. 6, (1972), pp. 503–522.
- [13] D. Mumford: The Red Book of varieties and schemes, Springer L.N.M. 1358, 1988. Zbl0658.14001
- [14] A. Weil: “Théorie des points proches sur les varietés différentiables”, Colloque Top. et Géom. Diff., Stasbourg 1953. Zbl0053.24903