共查询到20条相似文献,搜索用时 15 毫秒
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In this paper, we show the relation between the existence of twisted conical K?hler-Ricci solitons and the greatest log Bakry-Emery-Ricci lower bound on Fano manifolds. This is based on our proofs of some openness theorems on the existence of twisted conical K?hler-Ricci solitons, which generalize Donaldson’s existence conjecture and the openness theorem of the conical K?hler-Einstein metrics to the conical soliton case. 相似文献
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We prove the convergence of Kähler-Ricci flow with some small initial curvature conditions. As applications, we discuss the convergence of Kähler-Ricci flow when the complex structure varies on a Kähler-Einstein manifold. 相似文献
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Ryosuke Takahashi 《Mathematische Zeitschrift》2015,281(3-4):1021-1034
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In this paper, we consider orthogonal Ricci curvature \(Ric^{\perp }\) for Kähler manifolds, which is a curvature condition closely related to Ricci curvature and holomorphic sectional curvature. We prove comparison theorems and a vanishing theorem related to these curvature conditions, and construct various examples to illustrate subtle relationship among them. As a consequence of the vanishing theorem, we show that any compact Kähler manifold with positive orthogonal Ricci curvature must be projective. This result complements a recent result of Yang (RC-positivity, rational connectedness, and Yau’s conjecture. arXiv:1708.06713) on the projectivity under the positivity of holomorphic sectional curvature. The simply-connectedness is shown when the complex dimension is smaller than five. Further study of compact Kähler manifolds with \(Ric^{\perp }>0\) is carried in Ni et al. (Manifolds with positive orthogonal Ricci curvature. arXiv:1806.10233). 相似文献
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Let (X,D) be a polarized log variety with an effective holomorphic torus action, and Θ be a closed positive torus invariant (1,1) -current. For any smooth positive function g defined on the moment polytope of the torus action, we study the Monge-Ampère equations that correspond to generalized and twisted Kähler-Ricci g-solitons. We prove a version of the Yau-Tian-Donaldson (YTD) conjecture for these general equations, showing that the existence of solutions is always equivalent to an equivariantly uniform Θ-twisted g-Ding-stability. When Θ is a current associated to a torus invariant linear system, we further show that equivariant special test configurations suffice for testing the stability. Our results allow arbitrary klt singularities and generalize most of previous results on (uniform) YTD conjecture for (twisted) Kähler-Ricci/Mabuchi solitons or Kähler-Einstein metrics. © 2022 Wiley Periodicals, Inc. 相似文献
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Chao Xu 《中国科学 数学(英文版)》2010,53(11):3027-3036
In this paper, the author has considered the hyperbolic Khler-Ricci flow introduced by Kong and Liu, that is, the hyperbolic version of the famous Khler-Ricci flow. The author has explained the derivation of the equation and calculated the evolutions of various quantities associated with the equation including the curvatures. Particularly on Calabi-Yau manifolds, the equation can be simplifled to a scalar hyperbolic Monge-Ampère equation which is the hyperbolic version of the corresponding one in Khler-Ricci flow. 相似文献
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In this work, we will verify some comparison results on K?hler manifolds. They are: complex Hessian comparison for the distance function from a closed complex submanifold of a K?hler manifold with holomorphic bisectional curvature bounded below by a constant, eigenvalue comparison and volume comparison in terms of scalar curvature. This work is motivated by comparison results of Li and Wang (J Differ Geom 69(1):43–47, 2005). 相似文献
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Gideon Maschler 《Annals of Global Analysis and Geometry》2008,34(4):367-380
On a manifold of dimension at least six, let (g, τ) be a pair consisting of a Kähler metric g which is locally Kähler irreducible, and a nonconstant smooth function τ. Off the zero set of τ, if the metric \({\widehat{g}=g/\tau^{2}}\) is a gradient Ricci soliton which has soliton function 1/τ, we show that \({\widehat{g}}\) is Kähler with respect to another complex structure, and locally of a type first described by Koiso, and also Cao. Moreover, τ is a special Kähler–Ricci potential, a notion defined in earlier works of Derdzinski and Maschler. The result extends to dimension four with additional assumptions. We also discuss a Ricci–Hessian equation, which is a generalization of the soliton equation, and observe that the set of pairs (g, τ) satisfying a Ricci–Hessian equation is invariant, in a suitable sense, under the map \({(g,\tau) \rightarrow (\widehat{g},1/\tau)}\) . 相似文献
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Nefton Pali 《Mathematische Zeitschrift》2014,276(1-2):173-189
We show a quite simple second variation formula for Perelman’s $\mathcal W $ -functional along the modified Kähler-Ricci flow over Fano manifolds. 相似文献
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A classical result of McDuff [14] asserts that a simply connected complete Kähler manifold $(M,g,\omega )$ with non positive sectional curvature admits global symplectic coordinates through a symplectomorphism $\Psi \ : M \rightarrow \mathbb{R }^{2n}$ (where $n$ is the complex dimension of $M$ ), satisfying the following property (proved by E. Ciriza in [4]): the image $\Psi (T)$ of any complex totally geodesic submanifold $T\subset M$ through the point $p$ such that $\Psi (p)=0$ , is a complex linear subspace of $\mathbb C ^n\simeq \mathbb{R }^{2n}$ . The aim of this paper is to exhibit, for all positive integers $n$ , examples of $n$ -dimensional complete Kähler manifolds with non-negative sectional curvature globally symplectomorphic to $\mathbb{R }^{2n}$ through a symplectomorphism satisfying Ciriza’s property. 相似文献
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We show that the generalized Kähler–Ricci soliton equation on $4$ -dimensional toric Kähler orbifolds reduces to ODEs assuming there is a Hamiltonian $2$ -form. This leads to an explicit resolution of this equation on labelled triangles and convex labelled quadrilaterals. In particular, we give the explicit expression of the Kähler–Ricci solitons of weighted projective planes as well as new examples. 相似文献
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Greg Friedman 《Mathematische Annalen》2009,343(2):371-395
Cohen, Goresky, and Ji showed that there is a Künneth theorem relating the intersection homology groups to and , provided that the perversity satisfies rather strict conditions. We consider biperversities and prove that there is a Künneth theorem relating to and for all choices of and . Furthermore, we prove that the Künneth theorem still holds when the biperversity p, q is “loosened” a little, and using this we recover the Künneth theorem of Cohen–Goresky–Ji. 相似文献
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We discuss algebraic properties for the symbols of geometric first order differential operators on Kähler manifolds. Through a study of the universal enveloping algebra and higher Casimir elements, we know a lot of relations for the symbols, which induce Bochner identities for the operators. As applications, we have vanishing theorems, eigenvalue estimates, and so on. 相似文献
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