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

Kossowski, Marek

doi:10.1090/S0002-9939-1990-1013972-5

Lower bounds for the extrinsic total curvatures of a space-like codimension $2$ surface in Minkowski space
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Proc. Amer. Math. Soc. 109 (1990), 787-795 Request permission

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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Battille Recontares

Total curvature in Riemannian geometry