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Kaehler流形的Sasaki子流形 总被引:1,自引:0,他引:1
Kaehler流形是偶维微分流形,奇维微分流形中,与之媲美的是Sasaki流形。它是正规、切触度量流形。关于Sasaki流形,有判别定理(见[1]中P_(272)定理5.1) 定理A 殆切触度量流形M是Sasaki流形的充要条件为 (xφ)Y=g(X,Y)ξ-g(Y,ξ)X。 (1) 我们知道,Kaehler流形的Sasaki实超曲面是Sasaki流形,其维数也是奇数。Bejancu成功地对Kaehler流形的反全纯子流形引入Sasaki结构,定义了Sasaki反全纯子流形,其维 相似文献
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采用活动标架法,研究了四元数射影空间中的Willmore拉格朗日子流形的问题,得到了该空间中n维紧致Willmore拉格朗日子流形的Simons型积分不等式和刚性定理.这些定理将Willmore拉格朗日子流形的研究从复空间形式推广到了四元数射影空间. 相似文献
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微分几何中的BOCHNER技巧(下) 总被引:1,自引:0,他引:1
§3.紧致条件下的一些结果 这一节,我们讨论关于紧Riemann流形的几个定理,这些定理的证明都要借助于Bochner技巧.这里我们也要提到调和旋量的消灭定理,但进一步详细讨论要放到第5节,因为在讲述它时需要补充一些其它的预备知识. 在接触具体结果之前,我们先要做两点一般性说明.一点是,本节所有的定理从根本上都有赖于E.Hopf的广义极大值原理.(参看[YB]第26页;或[CH]326页).为把事情完全讲清楚,我们把这一原理整个重讲一遍.设P为定义在R~n的开子集U上的二阶线性椭圆算子,不带常数项,即 相似文献
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本文研究了完备非紧且Ricci曲率正有界的n维K(a)hler流形上的单值化问题,利用Sobolev不等式,L2估计和Bézout估计和Gauss-Bonnet积分方法,得到了一个单值化定理,推广了流形为有限拓扑型的结果. 相似文献
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1.二个同维数的光滑流形之间,映射的体积元之比是映射的最简单、最重要的度量不变量。陈省身教授[1]讨论了同维数 Hermitian 流形间和乐映射的减小体积性质,推广了著名的 Schwarz 引理,陈省身和 Goldberg[2]又对同维数实黎曼流形间的调和映射作了研究,得到若干减小体积的定理。本文将考虑二个不同维数的黎曼流形间的调和映射,以便推广[2]中有关的结论。 相似文献
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In this paper, we prove a local odd dimensional equivariant family index theorem which generalizes Freed's odd dimensional index formula. Then we extend this theorem to the noncommutative geometry framework. As a corollary, we get the odd family Lichnerowicz vanishing theorem and the odd family Atiyah-Hirzebruch vanishing theorem. 相似文献
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For a variety where a connected linear algebraic group acts with only finitely many orbits, each of which admits an attractive
slice, we show that the stratification by orbits is perfect for equivariant intersection cohomology with respect to any equivariant
local system. This applies to provide a relationship between the vanishing of the odd dimensional intersection cohomology
sheaves and of the odd dimensional global intersection cohomology groups. For example, we show that odd dimensional intersection
cohomology sheaves and global intersection cohomology groups vanish for all complex spherical varieties.
Received: 25 February 2000 / Accepted: 15 February 2001 / Published online: 23 July 2001 相似文献
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In this paper we introduce certain basic notions concerning infinite dimensional complex manifolds, and prove that the Dolbeault cohomology groups of infinite dimensional projective spaces, with values in finite rank vector bundles, vanish. Some applications of such vanishing theorems are discussed; e.g., we classify vector bundles of finite rank over infinite dimensional projective spaces. Finally, we prove a sharp theorem on solving the inhomogeneous Cauchy-Riemann equations on affine spaces.
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On the CR Poincaré–Lelong Equation,Yamabe Steady Solitons and Structures of Complete Noncompact Sasakian Manifolds
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In this paper, we solve the so-called CR Poincaré–Lelong equation by solving the CR Poisson equation on a complete noncompact CR(2n + 1)-manifold with nonegative pseudohermitian bisectional curvature tensors and vanishing torsion which is an odd dimensional counterpart of K?hler geometry. With applications of this solution plus the CR Liouvelle property, we study the structures of complete noncompact Sasakian manifolds and CR Yamabe steady solitons. 相似文献
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Shin-ichi Matsumura 《Mathematische Annalen》2014,359(3-4):785-802
The purpose of this paper is to establish Nadel type vanishing theorems with multiplier ideal sheaves of singular metrics admitting an analytic Zariski decomposition (such as, metrics with minimal singularities and Siu’s metrics). For this purpose, we generalize Kollár’s injectivity theorem to an injectivity theorem for line bundles equipped with singular metrics, by making use of the theory of harmonic integrals. Moreover we give asymptotic cohomology vanishing theorems for high tensor powers of line bundles. 相似文献
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Gregório Pacelli Bessa Leandro F. Pessoa Marco Rigoli 《Israel Journal of Mathematics》2018,226(2):703-736
In this paper we study non-compact self-shrinkers first in general codimension and then in codimension 1. We respectively prove some vanishing theorems giving rise to rigidity of the self-shrinker and then estimates involving the higher order mean curvatures for the oriented case. The paper ends with some results on their index when considered as appropriate \(\bar f\)-minimal hypersurfaces. 相似文献
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By using chaos expansion into multiple stochastic integrals, we make a wavelet analysis of two self-similar stochastic processes: the fractional Brownian motion and the Rosenblatt process. We study the asymptotic behavior of the statistic based on the wavelet coefficients of these processes. Basically, when applied to a non-Gaussian process (such as the Rosenblatt process) this statistic satisfies a non-central limit theorem even when we increase the number of vanishing moments of the wavelet function. We apply our limit theorems to construct estimators for the self-similarity index and we illustrate our results by simulations. 相似文献
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We introduce the notion of Hermitian Higgs bundle as a natural generalization of the notion of Hermitian vector bundle and we study some vanishing theorems concerning Hermitian Higgs bundles when the base manifold is a compact complex manifold. We show that a first vanishing result, proved for these objects when the base manifold was Kähler, also holds when the manifold is compact complex. From this fact and some basic properties of Hermitian Higgs bundles, we conclude several results. In particular we show that, in analogy to the classical case, there are vanishing theorems for invariant sections of tensor products of Higgs bundles. Then, we prove that a Higgs bundle admits no nonzero invariant sections if there is a condition of negativity on the greatest eigenvalue of the Hitchin–Simpson mean curvature. Finally, we prove that the invariant sections of certain tensor products of a weak Hermitian–Yang–Mills Higgs bundle are all parallel in the classical sense. 相似文献
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Osamu Fujino 《Mathematische Zeitschrift》2007,257(3):631-641
We use multiplication maps to give a characteristic-free approach to vanishing theorems on toric varieties. Our approach is
very elementary but is enough powerful to prove vanishing theorems. 相似文献
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We study an asymptotically linear elliptic equation at resonance, with an odd nonlinearity. By a penalization technique and
suitable min-max theorems (which give Morse index estimates), we prove the existence of pairs of non trivial solutions, where N is, roughly speaking, the difference between the Morse indexes at zero and at infinity.
Received December 1999 相似文献