共查询到20条相似文献,搜索用时 15 毫秒
1.
本文中。我们讨论K?hler流形上的Lagrange向量场,并用它来描述和解决Khler流形上的Newton力学和Lagrange力学中的一些问题。 相似文献
2.
《数学学报》2019,(5)
正Local Nonautonomous Schrodinger Flows on Kahler Manifolds Zong Lin JIA You De WANG Abstract In this paper,we prove that the nonautonomous Schrodinger flow from a compact Riemannian manifold into a Kahler manifold admits a local solution.Under some certain conditions,the solution is unique and has higher regularity. 相似文献
3.
In this paper we show that there exists a unique local smooth solution for the Cauchy problem of the Schrodinger flow for maps from a compact Riemannian manifold into a complete Kahler manifold, or from a Euclidean space Rm into a compact Kahler manifold. As a consequence, we prove that Heisenberg spin system is locally well-posed in the appropriate Sobolev spaces. 相似文献
4.
ZHONG Chunping & ZHONG Tongde School of Mathematical Sciences Xiamen University Xiamen China Department of Mathematics Zhejiang University Hangzhou China 《中国科学A辑(英文版)》2006,(11)
Faran posed an open problem about analysis on complex Finsler spaces: Is there an analogue of the (?)-Laplacian? Is there an analogue of Hodge theory? Under the assumption that (M,F) is a compact strongly Kahler Finsler manifold, we define a (?)-Laplacian on the base manifold. Our result shows that the well-known Hodge decomposition theorem in Kahler manifolds is still true in the more general compact strongly Kahler Finsler manifolds. 相似文献
5.
There is a well-known way to generalize the Riemann-Roch operator for Kahler manifold to that for Hermitian manifold. In this paper we show a slightly different way to get a generalized Riemann-Roch operator, which is just the Dirac operator. The difference between the two operators is that the latter one enables the so-called Pythagoras equalities. 相似文献
6.
In this paper, the authors prove that if Mn is a complete noncompact Kahler manifold with a pole p, and its holomorphic bisectional curvature is asymptotically non-negative to p, then it is a Stein manifold. 相似文献
7.
Juan-Pablo Ortega 《Comptes Rendus Mathematique》2002,334(11):999-1004
During the last thirty years, symplectic or Marsden–Weinstein reduction has been a major tool in the construction of new symplectic manifolds and in the study of mechanical systems with symmetry. This procedure has been traditionally associated to the canonical action of a Lie group on a symplectic manifold, in the presence of a momentum map. In this Note we show that the symplectic reduction phenomenon has much deeper roots. More specifically, we will find symplectically reduced spaces purely within the Poisson category under hypotheses that do not necessarily imply the existence of a momentum map. In other words, the right category to obtain symplectically reduced spaces is that of Poisson manifolds acted upon canonically by a Lie group. To cite this article: J.-P. Ortega, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 999–1004. 相似文献
8.
本文首先给出非正规化Khler-Ricci流下曲率的发展方程,然后得到了关于曲率的Harnack量在满足曲率局部条件下所产生的一个特殊项CNS.通过对CNS的估计,得到了完备Khler流形上关于Khler-Ricci流的局部Harnack不等式.最后,作为主要定理的应用,我们将结果推广到数量曲率的情形. 相似文献
9.
We show that a small neighborhood of a closed symplectic
submanifold in a geometrically bounded aspherical symplectic manifold has
non-vanishing symplectic homology. As a consequence, we establish the existence
of contractible closed characteristics on any thickening of the boundary
of the neighborhood. When applied to twisted geodesic flows on compact
symplectically aspherical manifolds, this implies
the existence of contractible periodic orbits for a dense set of
low energy values. 相似文献
10.
For any complete noncompact Kahler manifold with nonnegative and bounded holomorphic bisectional curvature, we provide the necessary and sufficient condition for the immortal solution to the Ricci flow. 相似文献
11.
本文给出了强Khler-Finsler流形上中值Laplace算子的一些性质,如自伴性质,散度形式等。与Khler流形上利用逆变基本张量及其在Finsler流形上的变形作为密度函数定义流形上的逐点内积及整体内积不同,作者利用强Khler-Finsler流形上的逆变密切Khler度量作为密度函数定义了流形上的逐点内积和整体内积,并定义了强Khler-Finsler流形上的Hodge-Laplace算子,它可看作函数情形中值Laplace算子的推广。 相似文献
12.
本文证明了任一n维的非紧完备,具有有限拓扑型的Kahler流形,若它的Ricci曲率为正的,有限的且陈氏示性数有限,则它双全纯等价于拟射影代数簇. 相似文献
13.
Xiaoli Chao Ranran Chen 《逼近论及其应用》2008,(3):292-302
We discuss a class of complete Kaihler manifolds which are asymptotically complex hyperbolic near infinity. The main result is vanishing theorems for the second L2 cohomology of such manifolds when it has positive spectrum. We also generalize the result to the weighted Poincare inequality case and establish a vanishing theorem provided that the weighted function p is of sub-quadratic growth of the distance function. We also obtain a vanishing theorem of harmonic maps on manifolds which satisfies the weighted Poincare inequality. 相似文献
14.
Jarek Kedra 《Differential Geometry and its Applications》2009,27(4):455-463
A symplectic form is called hyperbolic if its pull-back to the universal cover is a differential of a bounded one-form. The present paper is concerned with the properties and constructions of manifolds admitting hyperbolic symplectic forms. The main results are:
- • If a symplectic form represents a bounded cohomology class then it is hyperbolic.
- • The symplectic hyperbolicity is equivalent to a certain isoperimetric inequality.
- • The fundamental group of symplectically hyperbolic manifold is non-amenable.
Keywords: Symplectic manifold; Isoperimetric inequality; Bounded cohomology 相似文献
15.
设M是复流形,具有复(α,β)度量F=αφ(|β|/α),其中α为M上的Hermite度量,β为M上的(1,0)形式。本文得到与F相联系的复非线性联络系数Гiμ^i的表达式,且证明了:若β为M上的全纯(1,0)形式,并且关于α的Hermite联络γij^k(z)平行,则F是M上的复Berwald度量;若α是M上的Kaihler度量,则F是M上的强Kahler Finsler度量. 相似文献
16.
We have studied the normality of an almost contact metric hypersurface of a Kahler manifold. Quasi-umbilical and umbilical properties have also been studied. 相似文献
17.
Hermitian structures on six-dimensional nilmanifolds 总被引:2,自引:1,他引:1
Luis Ugarte 《Transformation Groups》2007,12(1):175-202
Let (J,g) be a Hermitian structure on a six-dimensional compact nilmanifold M with invariant complex structure J and compatible
metric g, which is not required to be invariant. We show that, up to equivalence of the complex structure, the strong
Kahler with torsion structures (J,g) on M are parametrized by the points in a subset of the Euclidean space, in particular,
the region inside a certain ovaloid corresponds to such structures on the Iwasawa manifold and the region outside to strong
Kahler with torsion structures with nonabelian J on the nilmanifold
where H3 is the Heisenberg group. A classification of six-dimensional nilmanifolds admitting balanced Hermitian structures (J,g) is
given, and as an application we classify the nilmanifolds having invariant complex structures which do not admit Hermitian
structure with restricted holonomy of the Bismut connection contained in SU(3). It is also shown that on the nilmanifold
the balanced condition is not stable under small deformations. Finally, we prove that a compact quotient of
where H(2,1) is the five-dimensional generalized Heisenberg group, is the only six-dimensional nilmanifold having locally
conformal Kahler metrics, and the complex structures underlying such metrics are all equivalent. Moreover, this nilmanifold
is a Vaisman manifold for any invariant locally conformal Kahler metric. 相似文献
18.
Let X be a compact symplectic manifold, K a compact group acting symplectically on X, and assume there is a moment map. In [3], Kirwan defined a stratification on X, and showed that the associated spectral sequence degenerates. In this note, we ask whether this degeneration comes from
a stable splitting of X into Thom spaces on the strata. One can also ask a related arithmetic question. Is it true that the splitting Kirwan discovered
respects the action of Galois groups?
Received: 20 March 1997 相似文献
19.
Kai Zehmisch 《Mathematische Zeitschrift》2014,277(1-2):285-291
We prove that if the unit codisc bundle of a closed Riemannian manifold embeds symplectically into a symplectic cylinder of radius one then the length of the shortest non-trivial closed geodesic is at most half the area of the unit disc. 相似文献
20.
In this paper, we consider the complex Monge-Ampère equation posed on a compact K?hler manifold. We show how to get L~p(p ∞) and L∞estimates for the gradient of the solution in terms of the continuity of the right-hand side. 相似文献