Conformal measures and locally conformally flat metric tensors
نویسندگان
چکیده
منابع مشابه
A 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 کاملGeometric 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 کاملTT - tensors and conformally flat structures on 3 - manifolds
We study transverse-tracefree (TT)-tensors on conformally flat 3-manifolds (M, g). The Cotton-York tensor linearized at g maps every symmetric tracefree tensor into one which is TT. The question as to whether this is the general solution to the TT-condition is viewed as a cohomological problem within an elliptic complex first found by Gasqui and Goldschmidt and reviewed in the present paper. Th...
متن کاملLocally conformal flat Riemannian manifolds with constant principal Ricci curvatures and locally conformal flat C-spaces
It is proved that every locally conformal flat Riemannian manifold all of whose Jacobi operators have constant eigenvalues along every geodesic is with constant principal Ricci curvatures. A local classification (up to an isometry) of locally conformal flat Riemannian manifold with constant Ricci eigenvalues is given in dimensions 4, 5, 6, 7 and 8. It is shown that any n-dimensional (4 ≤ n ≤ 8)...
متن کاملCompactness for Conformal Metrics with Constant Q Curvature on Locally Conformally Flat Manifolds
In this note we study the conformal metrics of constant Q curvature on closed locally conformally flat manifolds. We prove that for a closed locally conformally flat manifold of dimension n ≥ 5 and with Poincarë exponent less than n−4 2 , the set of conformal metrics of positive constant Q and positive scalar curvature is compact in the C∞ topology.
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: Annales Academiae Scientiarum Fennicae Mathematica
سال: 2016
ISSN: 1239-629X,1798-2383
DOI: 10.5186/aasfm.2016.4109