Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 44, No. 2, pp. 471-481 (2003)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



Holonomicity in synthetic differential geometry of jet bundles

Hirokazu Nishimura

Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki, Japan

Abstract: In the repetitive approach to the theory of jet bundles there are three methods of repetition, which yield non-holonomic, semi-holonomic, and holonomic jet bundles respectively. However the classical approach to holonomic jet bundles failed to be truly repetitive, for it must resort to such a non-repetitive coordinate-dependent construction as Taylor expansion. The principal objective in this paper is to give a purely repetitive definition of holonomicity by using microsquares (double tangents), which spells the flatness of the Cartan connection on holonomic infinite jet bundles without effort. The definition applies not only to formal manifolds but to microlinear spaces in general, enhancing the applicability of the theory of jet bundles considerably. The definition is shown to degenerate into the classical one in case of formal manifolds.

Full text of the article:

Electronic version published on: 1 Aug 2003. This page was last modified: 4 May 2006.

© 2003 Heldermann Verlag
© 2003--2006 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition