scholarly journals Maslov class rigidity for Lagrangian submanifolds via Hofer’s geometry

2010 ◽  
pp. 907-949 ◽  
Author(s):  
Ely Kerman ◽  
Nil Şirikçi
Keyword(s):  
Lagrangian Submanifolds ◽  
Maslov Class

SOME RESULTS ON GENERALIZED CALABI–YAU MANIFOLDS

2006 ◽  
Vol 03 (05n06) ◽  
pp. 1273-1292
Author(s):  
PAOLO DE BARTOLOMEIS ◽  
ADRIANO TOMASSINI
Keyword(s):  
Lagrangian Submanifolds ◽  
Lagrangian Submanifold ◽  
Dimensional Case ◽  
Maslov Class ◽  
Calabi Yau Manifolds

We consider generalized Calabi–Yau manifolds and we give a formula for the Maslov class of a Lagrangian submanifold of a generalized Calabi–Yau manifold. In particular, we characterize the Lagrangian submanifolds with vanishing Maslov class. In the 6-dimensional case, we refine our definition. Finally, we construct some examples.

ON THE MASLOV INDEX OF LAGRANGIAN SUBMANIFOLDS OF GENERALIZED CALABI–YAU MANIFOLDS

2006 ◽  
Vol 17 (08) ◽  
pp. 921-947 ◽  
Author(s):  
PAOLO DE BARTOLOMEIS ◽  
ADRIANO TOMASSINI
Keyword(s):  
Lagrangian Submanifolds ◽  
Maslov Index ◽  
Special Lagrangian ◽  
Maslov Class ◽  
Special Lagrangian Submanifolds ◽  
Calabi Yau Manifolds

We characterize the special Lagrangian submanifolds of a generalized Calabi–Yau manifold, with vanishing Maslov class. Then, we carefully describe several examples, including a non-Kähler generalized Calabi–Yau manifold foliated by special Lagrangian submanifolds.

scholarly journals -rigidity of Lagrangian submanifolds and punctured holomorphic disks in the cotangent bundle

2021 ◽  
Vol 157 (11) ◽  
pp. 2433-2493
Author(s):  
Cedric Membrez ◽  
Emmanuel Opshtein
Keyword(s):  
Cotangent Bundle ◽  
Symplectic Geometry ◽  
Homology Class ◽  
Lagrangian Submanifolds ◽  
Area Spectrum ◽  
Zero Section ◽  
Integral Homology ◽  
Cotangent Bundles ◽  
Maslov Class ◽  
Holomorphic Disks

Abstract Our main result is the $\mathbb {\mathcal {C}}^{0}$ -rigidity of the area spectrum and the Maslov class of Lagrangian submanifolds. This relies on the existence of punctured pseudoholomorphic disks in cotangent bundles with boundary on the zero section, whose boundaries represent any integral homology class. We discuss further applications of these punctured disks in symplectic geometry.

scholarly journals The Hörmander and Maslov Classes and Fomenko's Conjecture

1997 ◽  
Vol 4 (2) ◽  
pp. 185-200
Author(s):  
Z. Tevdoradze
Keyword(s):  
Lagrangian Submanifolds ◽  
Hermitian Manifold ◽  
Lagrangian Submanifold ◽  
Almost Hermitian Manifold ◽  
Maslov Class

Abstract Some functorial properties are studied for the Hörmander classes defined for symplectic bundles. The behavior of the Chern first form on a Lagrangian submanifold in an almost Hermitian manifold is also studied, and Fomenko's conjecture about the behavior of a Maslov class on minimal Lagrangian submanifolds is considered.

scholarly journals Linear Boundary Port Hamiltonian Systems defined on Lagrangian submanifolds

2020 ◽  
Vol 53 (2) ◽  
pp. 7734-7739
Author(s):  
Bernhard Maschke ◽  
Arjan van der Schaft
Keyword(s):  
Hamiltonian Systems ◽  
Lagrangian Submanifolds ◽  
Linear Boundary

On Lagrangian Catenoids

2007 ◽  
Vol 50 (3) ◽  
pp. 321-333 ◽  
Author(s):  
David E. Blair
Keyword(s):  
General Problem ◽  
Lagrangian Submanifolds ◽  
Minimal Submanifold ◽  
Conformally Flat ◽  
Totally Geodesic ◽  
Schouten Tensor ◽  
Multiplicity One

AbstractRecently I. Castro and F.Urbano introduced the Lagrangian catenoid. Topologically, it is ℝ × Sn–1 and its induced metric is conformally flat, but not cylindrical. Their result is that if a Lagrangian minimal submanifold in ℂn is foliated by round (n – 1)-spheres, it is congruent to a Lagrangian catenoid. Here we study the question of conformally flat, minimal, Lagrangian submanifolds in ℂn. The general problem is formidable, but we first show that such a submanifold resembles a Lagrangian catenoid in that its Schouten tensor has an eigenvalue of multiplicity one. Then, restricting to the case of at most two eigenvalues, we show that the submanifold is either flat and totally geodesic or is homothetic to (a piece of) the Lagrangian catenoid.

Minimal Lagrangian submanifolds in ℂP 3 and the sinh-Gordon equation

2001 ◽  
Vol 40 (1-4) ◽  
pp. 130-143 ◽  
Author(s):  
Ildefonso Castro ◽  
Luc Vrancken
Keyword(s):  
Gordon Equation ◽  
Lagrangian Submanifolds
Sign in / Sign up

Export Citation Format

Share Document