A geometric theory of harmonic and semi-conformal maps

• Autorzy: Anders Kock
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Harmonic; conformal; synthetic differential geometry; 51K10; 53A30; 53C43

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 5
• Strony: 708-724

Daty

wydano

2004-10-01

online

2004-10-01

Twórcy

autor

Anders Kock

• University of Aarhus

Bibliografia

• [1] P. Baird and J.C. Wood: Harmonic Morphisms Between Riemannian Manifolds, Oxford University Press, 2003.
• [2] E. Dubuc: “C ∞ schemes”, Am. J. Math, Vol. 103, (1981), pp. 683–690. http://dx.doi.org/10.2307/2374046
• [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).
• [7] A. Kock: “Infinitesimal aspects of the Laplace operator”, Theory and Applications of Categories Vol. 9(1), (2001).
• [8] A. Kock: “First neighbourhood of the diagonal, and geometric distributions”, Universitatis Iagellonicae Acta Math., Vol. 41. (2003), pp. 307–318.
• [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.
• [10] A. Kumpera and D. Spencer: “Lie Equations”, Annals of Math. Studies, Vol. 73, Princeton, 1972.
• [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.
• [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.
• [14] A. Weil: “Théorie des points proches sur les varietés différentiables”, Colloque Top. et Géom. Diff., Stasbourg 1953.

Identyfikatory

DOI

10.2478/BF02475972