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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Some properties of closed $1$-forms on a special Riemannian manifold


Author: Gr. Tsagas
Journal: Proc. Amer. Math. Soc. 81 (1981), 104-106
MSC: Primary 53C20
DOI: https://doi.org/10.1090/S0002-9939-1981-0589147-5
MathSciNet review: 589147
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Abstract: Let $M$ be a compact Riemannian manifold whose sectional curvature is strictly negative; then every closed $1$-form on $M$ has a singularity.


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Keywords: Riemannian manifold, closed <IMG WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$1$">-form, harmonic <IMG WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img3.gif" ALT="$1$">-form, negative <IMG WIDTH="15" HEIGHT="19" ALIGN="BOTTOM" BORDER="0" SRC="images/img10.gif" ALT="$\delta$">-pinched, singularity of <IMG WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$1$">-forms.
Article copyright: © Copyright 1981 American Mathematical Society