We solve the σ2-Yamabe problem for a non locally conformally flat manifold of dimension n > 8. Résumé : On résout le problème de σ2-Yamabe pour des variétés riemanniennes compactes sans bord non localement conformément plates de dimension n > 8. Dedicated to Professor W. Y. Ding on the occasion of his 60th birthday

In this paper, we prove a cohomology vanishing theorem on locally conformally flat manifold under certain positivity assumption on the Schouten tensor. And we show that this type of positivity of curvature is preserved under 0-surgeries for general Riemannian manifolds, and construct a large class of such manifolds.

In this note we study the problem of conformally flat structures bounding conformally flat structures and show that the eta invariants give obstructions. These lead us to the definition of an Abelian group, the conformal cobordism group, which classifies the conformally flat structures according to whether they bound conformally flat structures in a conformally invariant way. The eta invariant ...

dually flat finsler metrics form a special and valuable class of finsler metrics in finsler information geometry,which play a very important role in studying flat finsler information structure. in this paper, we prove that everylocally dually flat generalized randers metric with isotropic s-curvature is locally minkowskian.

Let (M, g) be a compact connected spin manifold of dimension n ≥ 3 whose Yamabe invariant is positive. We assume that (M, g) is locally conformally flat or that n ∈ {3, 4, 5}. According to a positive mass theorem by Schoen and Yau the constant term in the asymptotic development of the Green’s function of the conformal Laplacian is positive if (M, g) is not conformally equivalent to the sphere. ...

We derive a generalization of the flat space Yang's and Newman's equations for self-dual Yang-Mills fields to (locally) conformally Kahler Riemannian 4-manifolds. The results also apply Einstein metrics (whose full curvature is not necessarily self-dual). analyse possibility hidden symmetries in form Backlund transformations, we find continuous group only case which geometry half-flat. No isome...

In this paper, we prove the following two results: First, we study a class of conformally invariant operators P and their related conformally invariant curvatures Q on even-dimensional Riemannian manifolds. When the manifold is locally conformally flat(LCF) and compact without boundary, Q-curvature is naturally related to the integrand in the classical Gauss-Bonnet-Chern formula, i.e., the Pfaf...