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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 $ i(X)u = 0 = L(x)u$ is zero.


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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

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