Non-vanishing complex vector fields and the Euler characteristic
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- by Howard Jacobowitz PDF
- Proc. Amer. Math. Soc. 137 (2009), 3163-3165 Request permission
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
- 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
Additional Information
- Howard Jacobowitz
- Affiliation: Department of Mathematics, Rutgers University, Camden, New Jersey 08012
- MR Author ID: 190037
- Email: jacobowi@camden.rutgers.edu
- Received by editor(s): July 25, 2008
- Published electronically: May 1, 2009
- Communicated by: Varghese Mathai
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 3163-3165
- MSC (2000): Primary 57R25; Secondary 57R20
- DOI: https://doi.org/10.1090/S0002-9939-09-09915-8
- MathSciNet review: 2506476