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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Non-vanishing complex vector fields and the Euler characteristic


Author: Howard Jacobowitz
Journal: Proc. Amer. Math. Soc. 137 (2009), 3163-3165
MSC (2000): Primary 57R25; Secondary 57R20
Published electronically: May 1, 2009
MathSciNet review: 2506476
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. Michael F. Atiyah, Vector fields on manifolds, Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen, Heft 200, Westdeutscher Verlag, Cologne, 1970 (English, with German and French summaries). MR 0263102 (41 #7707)

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Additional Information

Howard Jacobowitz
Affiliation: Department of Mathematics, Rutgers University, Camden, New Jersey 08012
Email: jacobowi@camden.rutgers.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09915-8
PII: S 0002-9939(09)09915-8
Received by editor(s): July 25, 2008
Published electronically: May 1, 2009
Communicated by: Varghese Mathai
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.