Gap theorems for locally conformally flat manifolds
نویسندگان
چکیده
منابع مشابه
Geometric Inequalities on Locally Conformally Flat Manifolds
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...
متن کاملThe Scalar Curvature Deformation Equation on Locally Conformally Flat Manifolds
Abstract. We study the equation ∆gu− n−2 4(n−1)R(g)u+Ku p = 0 (1+ ζ ≤ p ≤ n+2 n−2 ) on locally conformally flat compact manifolds (M, g). We prove the following: (i) When the scalar curvature R(g) > 0 and the dimension n ≥ 4, under suitable conditions on K, all positive solutions u have uniform upper and lower bounds; (ii) When the scalar curvature R(g) ≡ 0 and n ≥ 5, under suitable conditions ...
متن کاملA Fully Nonlinear Conformal Flow on Locally Conformally Flat Manifolds
We study a fully nonlinear flow for conformal metrics. The long-time existence and the sequential convergence of flow are established for locally conformally flat manifolds. As an application, we solve the σk-Yamabe problem for locally conformal flat manifolds when k 6= n/2.
متن کاملBOUNDARIES OF LOCALLY CONFORMALLY FLAT MANIFOLDS IN DIMENSIONS 4k
We give global restrictions on the possible boundaries of compact, orientable, locally conformally flat manifolds of dimension 4k in terms of integrality of eta invariants.
متن کاملSchouten 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2016
ISSN: 0022-0396
DOI: 10.1016/j.jde.2015.09.027