Prescribed Schouten Tensor in Locally Conformally Flat Manifolds
نویسندگان
چکیده
منابع مشابه
Schouten curvature functions on locally conformally flat Riemannian manifolds
Consider a compact Riemannian manifold (M, g) with metric g and dimension n ≥ 3. The Schouten tensor Ag associated with g is a symmetric (0, 2)-tensor field describing the non-conformally-invariant part of the curvature tensor of g. In this paper, we consider the elementary symmetric functions {σk(Ag), 1 ≤ k ≤ n} of the eigenvalues of Ag with respect to g; we call σk(Ag) the k-th Schouten curva...
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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...
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ژورنال
عنوان ژورنال: Results in Mathematics
سال: 2019
ISSN: 1422-6383,1420-9012
DOI: 10.1007/s00025-019-1086-8