Skip to main content
SpringerLink
Log in

Fibrations spinorielles et twisteurs généralisés

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

Abstract

In the first part my purpose is to find existence conditions for a spin structure on a manifold in a purely differential geometric scope, without the machinery of the algebraic topology and avoiding systematically any matricial formalism.

A spin structure can be considered as aG-structure (using a classical terminology). Groups, called by myself “groups of spinoriality” play an essential part in this problem. We study them with a few details in the second part of chapter I.

The second part is devoted to introduce the notion of twistors, generalizing studies already made in particular cases. Twistorial fibrations naturally go with spin fibrations.

Broadly, twistors of order 2 are for the conformal group of signature (p, q), that are spinors for the group of isometry of signature (p+1,q+1).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Références

  1. M. F. Atiyah, R. Bott etA. Shapiro, Clifford modules,Topology 3 (1964),suppl. 1, 3–38.

    Article  MathSciNet  MATH  Google Scholar 

  2. Ch. Barbance,Thèse, Paris, 1969.

  3. C. Chevalley,The algebraic theory of spinors, Columbia University Press, New York, 1954.

    MATH  Google Scholar 

  4. A. Crumeyrolle, Structures spinorielles,Ann. Inst. H. Poincaré Sect. A (N. S.) 11 (1969), 19–55.

    MathSciNet  MATH  Google Scholar 

  5. A. Crumeyrolle, Groupes de spinorialité,Ann. Inst. H. Poincaré Sect. A (N. S.) 14 (1971), 309–323.

    MathSciNet  MATH  Google Scholar 

  6. A. Crumeyrolle, Dérivations, formes et opérateurs usuels sur les champs spinoriels des variétés différentiables de dimension paire,Ann. Inst. H. Poincaré Sect. A (N. S.) 16 (1972), 171–201.

    MathSciNet  MATH  Google Scholar 

  7. Y. Choquet-Bruhat,Géométrie différentielle et systèmes extérieurs, Dunod, Paris, 1968.

    MATH  Google Scholar 

  8. R. Hermann,Vector bundles in mathematical physics, Vol. 1, W. A. Benjamin, Inc., New York, 1970.

    MATH  Google Scholar 

  9. Y. Kosmann,Dérivées de Lie des spineurs, Thèse, Paris, 1970;Ann. Mat. Pura Appl. 91 (1972), 317–395.

  10. A. Lichnerowicz, Champs spinoriels et propagateurs en relativité générale,Bull. Soc. Math. France 92 (1964), 11–100.

    MathSciNet  MATH  Google Scholar 

  11. A. Lichnerowicz,Théorie globale des connexions et des groupes d'holonomie, Cremonese, Rome, 1955.

    MATH  Google Scholar 

  12. R. S. Palais,Seminar on the Atiyah-Singer index theorem, chap. IV: Differential operators on vector bundles, Princeton University Press, Princeton, 1965.

    Book  MATH  Google Scholar 

  13. R. Penrose, Twistor algebra,J. Mathematical Phys. 8 (1967), 345–366.

    Article  MathSciNet  MATH  Google Scholar 

  14. N. E. Steenrod,The topology of fibre bundles, Princeton University Press, Princeton, 1951.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université Paul Sabatier, 118, Route de Narbonne, F-31 077, Toulouse Cedex, France

    A. Crumeyrolle

Authors
  1. A. Crumeyrolle
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Crumeyrolle, A. Fibrations spinorielles et twisteurs généralisés. Period Math Hung 6, 143–171 (1975). https://doi.org/10.1007/BF02018816

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02018816

Search

Navigation