Abstract
The classification of semi-parallel surfaces in Euclidean space (by Deprez 1985) and in Riemannian space forms (by Mercuri 1991) is extended to the case of time-like surfaces in Lorentzian spacetime forms. Existence and geometry of such surfaces are investigated, especially of the exceptional and minimal ones in de Sitter spacetimes; here the minimal surfaces are the subjects of the geometrical string theory.
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