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A kinematical description of infinitesimal deformations of the world sheet spanned in spacetime by a relativistic membrane is presented. This provides a framework for obtaining both the classical equations of motion and the equations describing infinitesimal deformations about solutions of these equations when the action describing the dynamics of this membrane is constructed using any local geometrical world sheet scalars. As examples, we consider a Nambu membrane, and an action quadratic in the extrinsic curvature of the world sheet.
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Capovilla et al. (1995) studied this question.
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