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Surfaces of zero mean curvature of mixed type in Minkowski space. (English. Russian original) Zbl 1076.53015

Izv. Math. 67, No. 2, 209-224 (2003); translation from Izv. Ross. Akad. Nauk Ser. Mat. 67, No. 2, 5-20 (2003).
In the paper zero mean curvature surfaces in the three dimensional Minkowski space \(\mathbb{R}_1^3\) are studied. The author determines the set of points on the surface where the transition from time-like to space-like part takes place. It is shown that the set corresponds to the transition from the ellipticity set to the hyperbolicity set of a differential equation. However there exist points on the surface where a transition in the solutions of the differential equation takes place which does not correspond to a transition from time-like to space-like parts of the surface. Under some weak assumptions, whose restriction of generality are not completely clear, the author characterizes the structure of the set of transition points from time-like to space-like completely.

MSC:

53A35 Non-Euclidean differential geometry
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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