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Spatial and Lorentzian surfaces in Robertson-Walker space times. (English) Zbl 1144.81324

Summary: Let \(L^4_1(f,c)=(I \times_f S, g^c_f)\) be a Robertson-Walker space time which does not contain any open subset of constant curvature. In this paper, we provide a general study of nondegenerate surfaces in \(L^4_1(f,c)\). First, we prove the nonexistence of marginally trapped surfaces with positive relative nullity. Then, we classify totally geodesic submanifolds. Finally, we classify the family of surfaces with parallel second fundamental form and the family of totally umbilical surfaces with parallel mean curvature vector.

MSC:

53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C80 Applications of global differential geometry to the sciences
83C15 Exact solutions to problems in general relativity and gravitational theory
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