Webα,β that is shown to be independent of the metric. We elementary prove that E α,β has compact leaves if and only if αm = βn for some integers m and n, namely in the elliptic case. In this case the leaves of E α,β give explicitly the elliptic fibration of H α,β WebOct 12, 2015 · and a classical result of Gauduchon [12] says that every Hermitian metric is conformal to a Gauduchon metric (uniquely up to scaling, when n>2). In particular, if we restrict our attention to Gauduchon metrics, then we cannot use non-trivial conformal changes. Motivated by Yau’s theorem, in 1984 Gauduchon [13, xIV.5] posed the …
Einstein-Weyl structures on complex manifolds and conformal …
WebA Vaisman metric on a compact manifold is unique, up to a constant multi-plier. The proof is due to P. Gauduchon ([Gl]). Definition 2.5. Let M be an LCK-manifold , g an LCK-metric, and 6 the cor-responding Lee form. The metric g is called Gauduchon metric if d*0 = 0. Theorem 2.6. ([Gl]) Let M be a compact LCK-manifold. Then M admits a WebNov 7, 2024 · The quaternionic Hermitian metric gcan be easily reconstructed from Ω and J. Indeed, for any x,y∈TI1,0(M), one has(1)2g(x,y‾)=Ω(x,J(y‾)). If dΩ=0, one has dωI=dωJ=dωK=0, and the manifold (M,I,J,K,g)is hyperkähler. There are two torsion-free connections that can be naturally introduced on a hypercomplex manifold. fleet farm heated water bowl
On some applications of Gauduchon metrics SpringerLink
WebGauduchon showed that there exists a unique Gauduchon metric up to scaling (when $n\geq 2$ ) in the conformal class of any Hermitian metric $\alpha$ . Motivated by … WebGauduchon [4], any conformal class of Hermitian metrics contains a unique (up to homothety) metric satisfying this condition. The condition ddcΩ = 0 is well known. The Hermitian manifolds with ddcΩ = 0 are called strong KT manifolds and arise as target spaces of classical (2,0)-supersymmetric sigma models with torsion (see e.g.[10]). WebJul 9, 2016 · We prove the long time existence and uniqueness of solutions to the parabolic Monge-Amp\`ere equation on compact almost Hermitian manifolds. ... We study the continuity equation of the Gauduchon metrics and establish its ... Therefore a necessary condition for a (1,l) form ( G I a ' r r ) I,,, Rlr dz' A d? to be the Ricci form of some Kahler ... fleet farm hermantown automotive