共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, an estimate of the constant scalar curvature of a compact non- minimal pseudo-umbilical Lagrangian submanifold in CP3 is obtained. As its application, we prove that compact Einstein pseudo-umbilical Lagrangian submanifolds in CP3 must be minimal. 相似文献
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Kenji Fukaya Yong-Geun Oh Hiroshi Ohta Kaoru Ono 《Selecta Mathematica, New Series》2011,17(3):609-711
This is a continuation of part I in the series of the papers on Lagrangian Floer theory on toric manifolds. Using the deformations
of Floer cohomology by the ambient cycles, which we call bulk deformations, we find a continuum of non-displaceable Lagrangian fibers on some compact toric manifolds. We also provide a method of finding
all fibers with non-vanishing Floer cohomology with bulk deformations in arbitrary compact toric manifolds, which we call
bulk-balanced Lagrangian fibers. 相似文献
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Tommaso Pacini 《Transactions of the American Mathematical Society》2003,355(8):3343-3357
Given a compact Riemannian manifold together with a group of isometries, we discuss MCF of the orbits and some applications: e.g., finding minimal orbits. We then specialize to Lagrangian orbits in Kaehler manifolds. In particular, in the Kaehler-Einstein case we find a relation between MCF and moment maps which, for example, proves that the minimal Lagrangian orbits are isolated.
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In this exposition, we show that the Hamiltonian is always constant on a compact invariant connected subset which lies in a Lagrangian graph provided that the Hamiltonian and the graph are sufficiently smooth. We also provide some counterexamples to show that if the Hamiltonian function is not smooth enough, then it may be non-constant on a compact invariant connected subset which lies in a Lagrangian graph. 相似文献
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For a Lagrangian torus A in a simply-connected projective symplectic manifold M, we prove that M has a hypersurface disjoint from a deformation of A. This implies that a Lagrangian torus in a compact hyperkähler manifold is a fiber of an almost holomorphic Lagrangian fibration, giving an affirmative answer to a question of Beauville’s. Our proof employs two different tools: the theory of action-angle variables for algebraically completely integrable Hamiltonian systems and Wielandt’s theory of subnormal subgroups. 相似文献
9.
New results on a class of exact augmented Lagrangians 总被引:3,自引:0,他引:3
S. Lucidi 《Journal of Optimization Theory and Applications》1988,58(2):259-282
In this paper, a new continuously differentiable exact augmented Lagrangian is introduced for the solution of nonlinear programming problems with compact feasible set. The distinguishing features of this augmented Lagrangian are that it is radially unbounded with respect to the multiplier and that it goes to infinity on the boundary of a compact set containing the feasible region. This allows one to establish a complete equivalence between the unconstrained minimization of the augmented Lagrangian on the product space of problem variables and multipliers and the solution of the constrained problem.The author wishes to thank Dr. L. Grippo for having suggested the topic of this paper and for helpful discussions. 相似文献
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In this paper we construct a class of compact minimal Lagrangian submanifolds in complex hyperquadrics by studying Gauss maps of compact rotational hypersurfaces in the unit sphere. 相似文献
11.
Yat-Ming Chan 《Annals of Global Analysis and Geometry》2009,35(1):91-114
In this paper we extend our previous results on resolving conically singular Calabi–Yau 3-folds (Chan, Quart. J. Math. 57:151–181,
2006; Quart. J. Math., to appear) to include the desingularizations of special Lagrangian (SL) 3-folds with conical singularities
that occur at the same points of the ambient Calabi–Yau. The gluing construction of the SL 3-folds is achieved by applying
Joyce’s analytic result (Joyce, Ann. Global. Anal. Geom. 26: 1–58, 2004, Thm. 5.3) on deforming Lagrangian submanifolds to
nearby special Lagrangian submanifolds. Our result will in principle be able to construct more examples of compact SL submanifolds
in compact Calabi–Yau manifolds. Various explicit examples and applications illustrating the result in this paper can be found
in the sequel (Chan, Ann. Global. Anal. Geom., to appear). 相似文献
12.
The n-dimensional complex hyperquadric is a compact complex algebraic hypersurface defined by the quadratic equation in the (n+1)-dimensional complex projective space, which is isometric to the real Grassmann manifold of oriented 2-planes and is a
compact Hermitian symmetric space of rank 2. In this paper, we study geometry of compact Lagrangian submanifolds in complex
hyperquadrics from the viewpoint of the theory of isoparametric hypersurfaces in spheres. From this viewpoint we provide a
classification theorem of compact homogeneous Lagrangian submanifolds in complex hyperquadrics by using the moment map technique.
Moreover we determine the Hamiltonian stability of compact minimal Lagrangian submanifolds embedded in complex hyperquadrics
which are obtained as Gauss images of isoparametric hypersurfaces in spheres with g(= 1, 2, 3) distinct principal curvatures.
Dedicated to Professor Hajime Urakawa on his sixtieth birthday.
H. Ma was partially supported by NSFC grant No. 10501028, SRF for ROCS, SEM and NKBRPC No. 2006CB805905. Y. Ohnita was partially
supported by JSPS Grant-in-Aid for Scientific Research (A) No. 17204006. 相似文献
13.
Given a compact Lagrangian submanifold in flat space evolving by its mean curvature, we prove uniform
-bounds in space and C2-estimates in time for the underlying Monge-Ampére equation under weak and natural assumptions on the initial Lagrangian submanifold. This implies longtime existence and convergence of the Lagrangian mean curvature flow. In the 2-dimensional case we can relax our assumptions and obtain two independent proofs for the same result.Received: 3 September 2002, Accepted: 12 June 2003, Published online: 4 September 2003Mathematics Subject Classification (2000):
53C44 相似文献
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For any irreducible compact homogeneous Kähler manifold, we classify the compact tight Lagrangian submanifolds which have the ?2-homology of a sphere. 相似文献
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Knut Smoczyk 《Mathematische Zeitschrift》2002,240(4):849-883
We prove that symplectic maps between Riemann surfaces L, M of constant, nonpositive and equal curvature converge to minimal symplectic maps, if the Lagrangian angle for the corresponding Lagrangian submanifold in the cross product space satisfies . If one considers a 4-dimensional K?hler-Einstein manifold of nonpositive scalar curvature that admits two complex structures J, K which commute and assumes that is a compact oriented Lagrangian submanifold w.r.t. J such that the K?hler form w.r.t.K restricted to L is positive and , then L converges under the mean curvature flow to a minimal Lagrangian submanifold which is calibrated w.r.t. .
Received: 11 April 2001 / Published online: 29 April 2002 相似文献
16.
Daniele Sepe 《Geometriae Dedicata》2010,149(1):347-362
This paper completes the classification of regular Lagrangian fibrations over compact surfaces. Mishachev (Diff Geom Appl
6:301–320, 1996) classifies regular Lagrangian fibrations over
\mathbbT2{\mathbb{T}^2}. The main theorem in Fried et al. (Comment Math Helv 56(4):487–523, 1981) is used to in order to classify integral affine
structures on the Klein bottle K
2 and, hence, regular Lagrangian fibrations over this space. 相似文献
17.
Maria Luiza LAPA DE Souza 《K-Theory》2002,25(3):233-249
We construct two cohomological invariants associated to pairs of Lagrangian sub-bundles of a symplectic bundle on a compact manifold upon which a compact Lie group is acting. The first invariant, which we call the classical equivariant Maslov H-invariant, provides an obstruction to Lagrangian transversality and lives in the Borel cohomology. The second invariant, which we call the equivariant Maslov U-invariant, generalises the author's results in K-Theory 13 (1998), 347–361 to the equivariant context and provides a necessary and sufficient condition for equivariant Lagrangian transversality, up to homotopic stability, and lives in the U-theory (intermediate between the real complex K-theories). As an application, we show that two Lagrangian sub-bundles of a symplectic bundle on a homogeneous space are always stably transverse. 相似文献
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Fang Wang 《Journal of Differential Equations》2009,247(12):3258-3282
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Knut Smoczyk 《Calculus of Variations and Partial Differential Equations》1999,8(3):247-258
If is a Lagrangian manifold immersed into a K?hler-Einstein manifold, nothing is known about its behavior under the mean curvature
flow. As a first result we derive a Harnack inequality for the mean curvature potential of compact Lagrangian immersions immersed into .
Received March 16, 1997 / Accepted April 24, 1998 相似文献
20.
In this paper, we obtain several new characterizations of the Clifford torus as a Lagrangian self-shrinker. We first show that the Clifford torus \({\mathbb {S}}^1(1)\times {\mathbb {S}}^1(1)\) is the unique compact orientable Lagrangian self-shrinker in \({\mathbb {C}}^2\) with \(|A|^2\le 2\), which gives an affirmative answer to Castro–Lerma’s conjecture in Castro and Lerma (Int Math Res Not 6:1515–1527; 2014). We also prove that the Clifford torus is the unique compact orientable embedded Lagrangian self-shrinker with nonnegative or nonpositive Gauss curvature in \({\mathbb {C}}^2\). 相似文献