A concrete realization of the Milnor–Lichnerowicz spinor bundle by algebraic spinors is considered in the case when the holonomy group of the Levi‐Civita connection is equal to the Crumeyrolle group. Some relationships between the existence of parallel spinor fields on a space‐time manifold ℳ and its topological invariants are given.
REFERENCES
1.
C. Chevalley, The Algebraic Theory of Spinors (Columbia U.P., New York, 1954).
2.
D. Husemoller, Fibre Bundles (McGraw‐Hill, New York, 1966).
3.
A. Crumeyrolle, Algebresde Cliffordet Spineurs (Toulouse, 1979).
4.
5.
A. Lichnerowicz, C. R. Acad. Sci. Paris Ser A‐B 1963, 257.
6.
7.
8.
9.
10.
11.
H. Baum, Spin‐Structuren und Dirac‐Operatoren über pseudoriemannschen Mannigfaltigkeiten (Teubner, Leipzig, 1981), Band 41.
12.
13.
Th. Friedrich, Dissertation, Humboldt University, Berlin, 1978.
14.
P. Lounesto “On primitive idempotents of Clifford algebras,” Helsinki Report‐HTKK‐MAT‐A113, 1977.
15.
K. Bugajska, “Internal structure of space‐time,” submitted for publication.
16.
S. Kobayashi and K. Nomizu, Foundations of Differential Geometry (New York, Interscience, 1969), Vol. II.
17.
See Ref. 16, Vol. I (1963).
18.
B. Reinhart, Differential Geometry of Foliations (Springer, Berlin, 1983).
19.
F. Kamber and P. Tondeur, “Foliated bundles and characteristic classes,” in Lecture Notes in Mathematics, Vol. 493 (Springer, Berlin, 1975).
20.
21.
S. Sternberg, Lectures on Differential Geometry (Chelsea, New York, 1983), 2nd ed.
This content is only available via PDF.
© 1986 American Institute of Physics.
1986
American Institute of Physics
You do not currently have access to this content.
