Parallel submanifolds in pseudo-Euclidean spaces are characterized locally by the system ∇h = 0. Submanifolds satisfying the integrability condition R • h = 0 of this system are called semiparallel; geometrically they are 2nd-order envelopes of the parallel submanifolds. The existence and geometry of such two-dimensional Riemannian submanifolds (surfaces) are investigated and their complete classification is given. Moreover, it is shown that in E n s with s > 0 do exist not totally geodesic minimal semiparallel space-like surfaces.
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