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Proceedings of the American Mathematical Society

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

 

 

Curvature forms for Lorentz $ 2$-manifolds


Author: John T. Burns
Journal: Proc. Amer. Math. Soc. 63 (1977), 134-136
MSC: Primary 53C50
DOI: https://doi.org/10.1090/S0002-9939-1977-0470916-6
MathSciNet review: 0470916
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Abstract: As a converse to the Gauss-Bonnet theorem for Lorentz metrics on 2-manifolds, we show that if $ \bar \Omega $ is a 2-form on the torus $ {T^2}$ and $ {\smallint _{{T^2}}}\bar \Omega = 0$ then $ \bar \Omega $ is the curvature form of some Lorentz metric on $ {T^2}$.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0470916-6
Article copyright: © Copyright 1977 American Mathematical Society