Deformations of the scalar curvature

Fischer, A. E. and J. E. Marsden

Duke Math. J., 42, (1975), 519-547

Abstract:

Our main goal is to study the relationship between infinitesimal and actual perturbations of the scalar curvature function with respect to varying metric and to describe when solutions of the linearized equations can be used to approximate solutions of the nonlinear ones. Many of the results are motivated by corresponding questions in general relativity, Fischer and Marsden [17]. This paper supplies details and extensions of the results announced in Fischer and Marsden [19] and described in Fischer and Marsden [20]. The starting point of our proofs is the basic work of Ebin [14] and Berger-Ebin [4]. We begin with a few general notions.