Remarques sur les vari�t�s conform�ment plates

Codazzi Tensor Fields, Curvature and Pontryagin Forms

“…Then b = Ric-(2n-2)" 1 Scal.^f is a Codazzi tensor (non-trivial, unless {M,g) is of constant curvature). In fact, for n = 3, the Codazzi equation for b is equivalent to the conformal flatness of g, while, for n ^ 4, the Weyl conformal tensor W of any Riemannian nmanifold satisfies the well-known divergence formula [7,5,13]. In particular, such a metric always exists on the product S 1 xN, N being any compact Einstein manifold of positive scalar curvature.…”

Weakly Einstein Critical Point Equation

“…Lafontaine showed that the conjecture holds if a solution metric g is conformally flat and the kernel of s ′ * g is nontrivial, or ker s ′ * g = 0 [5]. Recently, Yun, Chang, and Hwang showed that the Besse conjecture is true for Riemannian manifolds with harmonic curvature [8].…”

Espaces twistoriels et structures complexes non standards

“…Soit M une surface minimale de dimension de Kodaira un spin et de caractéristique d'Euler nulle. Si M admet une métrique g anti-autoduale alors la métrique est localement conformément plate,à courbure scalaire (strictement) négative [7], non hermitienne [8], non Einstein età holonomie sans sous-espace invariant [26]. En particulier la métrique n'est pas Ricci parallèle.…”