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摘要
In this paper, we study conformally flat (alpha, beta)-metrics in the form F = alpha phi(beta/alpha), where a is a Riemannian metric and beta is a 1-form on a C-infinity manifold M. We prove that if phi = phi(s) is a polynomial in s, the conformally flat weak Einstein (alpha, beta)-metric must be either a locally Minkowski metric or a Riemannian metric. Moreover, we prove that conformally flat (alpha, beta)-metrics with isotropic S-curvature are also either locally Minkowski metrics or Riemannian metrics.
