Abstract
De Sitter space–time is considered to be represented by a D-dimensional hyperboloid embedded in (D+1)-dimensional Minkowski space–time. The string equation is derived from a string action which contains a Lagrange multiplier to restrict coordinates to de Sitter space–time. The string system of equations is equivalent to a type of generalized sinh–Gordon equation. The evolution equations for all the variables including the coordinates and their derivatives are obtained for D=2,3 and 4.
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