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Proceedings of the American Mathematical Society

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

 

 

Lower bounds for the extrinsic total curvatures of a space-like codimension $ 2$ surface in Minkowski space


Author: Marek Kossowski
Journal: Proc. Amer. Math. Soc. 109 (1990), 787-795
MSC: Primary 53C50
MathSciNet review: 1013972
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Abstract: There are three invariant curvature functions defined on any smooth space-like $ 2$-surfaces in four-dimensional Minkowski space. (If the surface lies in a Euclidean hyperplane then the functions agree with $ {H^2},{K^2}$, and $ {\left( {{H^2} - K} \right)^2}$. For each of these functions we show that there exists a space-like immersion of any oriented compact (or noncompact complete) surface with associated total curvature arbitrarily small.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1013972-5
Article copyright: © Copyright 1990 American Mathematical Society