Vector fields orthogonal to a nonvanishing infinitesimal isometry
Author:
Chao Chu Liang
Journal:
Proc. Amer. Math. Soc. 75 (1979), 326-328
MSC:
Primary 57R25; Secondary 53C21
DOI:
https://doi.org/10.1090/S0002-9939-1979-0532160-5
MathSciNet review:
532160
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Abstract: Let X be a nonvanishing infinitesimal isometry on a compact Riemannian manifold M. If there exists a nonvanishing vector field orthogonal to X and commuting with X, then the Euler characteristic of the complex consisting of all the differential forms u satisfying is zero.
- [1] M. F. Atiyah, Vector fields on manifolds, Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen, Heft 200, Westdeutscher Verlag, Cologne, 1970. MR 0263102 (41:7707)
- [2] -, Elliptic operators and compact groups, Lecture Notes in Math., vol. 401, Springer-Verlag, Berlin-Heidelberg-New York, 1974. MR 0482866 (58:2910)
- [3] W. Greub, S. Halperin and R. Vanstone, Connections, curvature, and cohomology. Vol. II, Academic Press, New York-London, 1973. MR 0400275 (53:4110)
- [4] B. L. Reinhart, Harmonic integrals on foliated manifolds, Amer. J. Math. 81 (1959), 529-536. MR 0107280 (21:6005)
- [5] G. W. Schwarz, On the de Rham cohomology of the leaf space of a foliation, Topology 13 (1974), 185-187. MR 0341503 (49:6254)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1979-0532160-5
Keywords:
Infinitesimal isometry,
vector fields,
transversally elliptic operators,
Euler characteristic
Article copyright:
© Copyright 1979
American Mathematical Society