Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Non-vanishing complex vector fields and the Euler characteristic

Author(s): Howard Jacobowitz
Journal: Proc. Amer. Math. Soc. 137 (2009), 3163-3165.
MSC (2000): Primary 57R25; Secondary 57R20
Posted: May 1, 2009
MathSciNet review: 2506476
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Abstract: Every manifold admits a nowhere vanishing complex vector field. If, however, the manifold is compact and orientable and the complex bilinear form associated to a Riemannian metric is never zero when evaluated on the vector field, then the manifold must have zero Euler characteristic.

References:

1.: Atiyah, M., Vector fields on manifolds. Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen, Heft 200, Westdeutscher Verlag, Cologne, 1970, 26 pp. MR 0263102 (41:7707)

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