Geometric Inequalities on Locally Conformally Flat Manifolds
نویسندگان
چکیده
In this paper, we are interested in certain global geometric quantities associated to the Schouten tensor and their relationship in conformal geometry. For an oriented compact Riemannian manifold (M,g) of dimension n > 2, there is a sequence of geometric functionals arising naturally in conformal geometry, which were introduced by Viaclovsky in [29] as curvature integrals of Schouten tensor. If we denote Ricg and Rg be the Ricci tensor and the scalar curvature of g respectively, the Schouten tensor can be written as
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