Tohoku Mathematical Journal

Une généralisation du calcul des jets et quelques prolongements généralisés de variétés différentiables

Michiaki Kawaguchi

Full-text: Open access

Article information

Source
Tohoku Math. J. (2), Volume 13, Number 2 (1961), 329-370.

Dates
First available in Project Euclid: 4 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178244307

Digital Object Identifier
doi:10.2748/tmj/1178244307

Mathematical Reviews number (MathSciNet)
MR0176412

Zentralblatt MATH identifier
0137.15001

Subjects
Primary: 53.40

Citation

Kawaguchi, Michiaki. Une généralisation du calcul des jets et quelques prolongements généralisés de variétés différentiables. Tohoku Math. J. (2) 13 (1961), no. 2, 329--370. doi:10.2748/tmj/1178244307. https://projecteuclid.org/euclid.tmj/1178244307


Export citation

References

  • [1] H. V. CRAIG: On tensors relative to the extended point transformation. Amer. J. M., 59 (1937), 764-774.
  • [2] H. V. CRAIG: On extensors and a Euclidean basis for higher order spaces, Amer.J. M., 61 (1937), 791-808.
  • [3] H. V. CRAIG: Vector and tensor analysis, McGraw-Hill Book Co., (1943)
  • [4] H. V. CRAIG: On the multiple parameter Jacobian extensor, Tensor N. S., 2 (1952), 27-35
  • [5] H. V. CRAIG: On certain linear extensor equations, Tensor, N. S., 4 (1954), 40-50
  • [6] H. V. CRAIG: On certain linear extensor equations II, Tensor, N. S., 5 (1955), 77-84
  • [7] H. V. CRAIG: On extensors first order partial differential equations and Poisson brackets, Tensor, N. S., 5 (1956), 159-164.
  • [1] CH. EHRESMANN: Les prolongements d'une variet defferentiable, Atti IV Congresso Unione mat Italiana, Taormina Ott, (1951), 1-9.
  • [2] CH. EHRESMANN: Les prolongements d'une variete differentiate, I. Calcul des jets, prolongemen princial, C. R. Ac. Sc., Paris, 233 (1951), 598-600.
  • [3] CH. EHRESMANN: Les prolongements d'une variete differentiate, II. L'espace des jets d'ordre r d Vn dans Vm C. R. Ac.Sc., Paris, 233 (1951), 777-779.
  • [4] CH. EHRESMANN: Les prolongements d'une variete differentiable, III. Transitivit des prolongements, C. R. Ac.Sc., Paris, 233 (1951), 1081-1083.
  • [5] CH. EHRESMANN: Structures locales et structures infinitesimales, C. R. Ac.Sc., Paris, 234 (1952), 587 589.
  • [6] CH. EHRESMANN: Les prolongements d'une variete differentiable, IV. Elements de contact et element d'enveloppe, C. R. Ac.Sc., Paris, 234 (1952), 1028-1030.
  • [7] CH. EHRESMANN: Les prolongements d'une variete differentiable, V. Covariants differentiels e prolongements d'une structure infinitesimale, C. R. Ac.Sc., Paris, 234 (1952), 1424-1425.
  • [8] CH. EHRESMANN: Introduction a la theorie des structures infinitesimales et des pseudo-groupes d Lie, Colloque intern. Geometrie differentielle de Strasbourg, C. N. R. S., (1953), 97-110.
  • [9] CH. EHRESMANN: Extension du calcul des jets aux jets non-holonomes, C. R. Ac.Sc., Paris, 23 (1954), 1762-1764.
  • [10] CH. EHRESMANN: Sur les structures infinitesimales regulieres, Proceedings intern. Congress of Math., Amsterdam (1954).
  • [11] CH. EHRESMANN: Applications de la notion de jet non holonome, C. R. Ac.Sc., Paris, 240 (1955), 397-399.
  • [12] CH. EHRESMANN: Les prolongements d'un espace fibre differentiate, C. R. Ac.Sc., Paris, 240 (1955) 1755-1757.
  • [13] CH. EHRESMANN: Les connexionsinfinitesimales d'ordre superieur, Dagli Atti des V Congresso del Union mat. Italiana, Pavia-Torino (1956), 1-3.
  • [1] H. HOMBU ET T. SUGURI: A treatment of geometric quantities in the manifold of surface-elements, Mem Fac.Sci., Kyusy Imp. Univ., Ser.A. 2 (1941), 67-90.
  • [1] A. KAWAGUCHI: Theory of Connections in a Kawaguchi space of higher order, Proc.Imp. Acad Tokyo, 13 (1937), 237-240.
  • [2] A. KAWAGUCHI: Einige Satze ber die Extensoren, Annales de la Societ Polonaise de Mathematique, 17 (1938), 166-176.
  • [3] A. KAWAGUCHI: Views on higher geometry of connections, Tensor, 1 (1938), 13-18
  • [4] A. KAWAGUCHI: Eiiie Verallgemeinerung von Extensoren, Monatsh., 48 (1939), 329-339
  • [5] A. KAWAGUCHI: Views on higher order geometry of connections, II, Tensor, 2 (1939), 39-45
  • [6] A. KAWAGUCHI: Die Differentialgeometrie hherer Ordnung I. Erweiterte Koordinatentransforma tionen und Extensoren, Jour.Fac.Sci, Hokkaido Imp. Univ., 9 (1940), 1-152.
  • [7] A. KAWAGUCHI: Views on higher order geometry of connections, III, Tensor, 3 (1940), 68-70
  • [8] A. KAWAGUCHI: Views on higher order geometry of connections, IV, Tensor, 4 (1941), 66-68
  • [9] A. KAWAGUCHI: Die Differentialgeometrie hoherer Ordnung III. Erweiterte Parametertransforma tionen und P-Tensoren, Jour.Fac.Sci., Hokkaido Imp. Univ., 10 (1941), 77-156.
  • [10] A. KAWAGUCHI: On the theory of non-linear connections I. Introduction to the theory of genera non-linear connections, Tensor, N. S., 2 (1952), 123-142.
  • [11] A. KAWAGUCHI: On the theory of non-linear connections, Convegno internazionale di Geom. Diff., (1953), 27-32.
  • [12] A. KAWAGUCHI: On the theory of non-linear connections II. Theory of Minkowski space and of non linear connections in a Finsler space, Tensor, N. S., 6 (1956) 165-199.
  • [13] A. KAWAGUCHI: Die Differentialgeometrie hoherer Ordnung IV, Erweiterung der verallgemeinerte Rheonomtransformation von Flachenelementen hoherer Ordnung undr-Extensoren, Publicationen Mathematicae, Debrecen, 7 (1960) 256-276.
  • [1] M. KAWAGUCHI: A generalization of the extensor, Tensor, N. S., 2 (1952), 59-66
  • [2] M. KAWAGUCHI: On a generalization of the multiple parameter extensor, Tensor, N. S., 2 (1952), 99-101.
  • [3] M. KAWAGUCHI: On some theorems in the ^--extensor analysis, Tensor, N. S., 3 (1953), 46-52
  • [4] M. KAWAGUCHI: Sur les derivees covariantes des £-extenseurs, Tensor, N. S., 11 (1961), 74-98
  • [5] M. KAWAGUCHI: An introduction to the theory of Kawaguchi spaces, R. A. A. G., 3°Series, No.33, (1960), 1-41.
  • [1] V. V. VAGNER: The theory of composite manifolds, Trudy Sem. Vektor, Tensor, Analizu, 8 (1960), 11-72.
  • [2] V. V. VAGNER: The geometry of the generalized Cartan spaces and the theory of geometric dif ferential objects, Doklady Akad. Nauk SSSR (N. S.), 77 (1951), 777-780.