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 | References | Similar Articles | Additional Information
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.
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- [2] Michael Francis Atiyah, Elliptic operators and compact groups, Lecture Notes in Mathematics, Vol. 401, Springer-Verlag, Berlin-New York, 1974. MR 0482866
- [3] Werner Greub, Stephen Halperin, and Ray Vanstone, Connections, curvature, and cohomology, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Volume III: Cohomology of principal bundles and homogeneous spaces; Pure and Applied Mathematics, Vol. 47-III. MR 0400275
- [4] Bruce L. Reinhart, Harmonic integrals on foliated manifolds, Amer. J. Math. 81 (1959), 529–536. MR 0107280, https://doi.org/10.2307/2372756
- [5] Gerald W. Schwarz, On the de Rham cohomology of the leaf space of a foliation, Topology 13 (1974), 185–187. MR 0341503, https://doi.org/10.1016/0040-9383(74)90008-1
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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
