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The equations of motion and boundary conditions for the fluctuations around aclassical open string, in a curved space-time with torsion, are considered incompact and world-sheet covariant form. The rigidly rotating open strings inAnti de Sitter space with and without torsion are investigated in detail. Bycarefully analyzing the tangential fluctuations at the boundary, we showexplicitly that the physical fluctuations (which at the boundary arecombinations of normal and tangential fluctuations) are finite, even though theworld-sheet is singular there. The divergent 2-curvature thus seems lessdangerous than expected, in these cases. The general formalism can bestraightforwardly used also to study the (bosonic part of the) fluctuationsaround the closed strings, recently considered in connection with the AdS/CFTduality, on AdS_5 \times S^5 and AdS_3 \times S^3 \times T^4.Comment: 19 pages, Late

Open string fluctuations in AdS space with and without torsion