The Equation of Prescribed Ricci Curvature
نویسندگان
چکیده
Introduction. In [5], J. Milnor cited "understanding the Ricci tensor Rik = J^ Rt'kl 9J as a fundamental problem of present-day mathematics. A basic issue, then, is to determine which symmetric covariant tensors of rank two can be Ricci tensors of Riemannian metrics. The definition of Ricci curvature casts the problem of finding a metric g which realizes a given Ricci curvature R as one of solving a system of nonlinear second-order partial differential equations for g. We write these equations as
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