scholarly journals Holomorphic Lagrangian subvarieties in holomorphic symplectic manifolds with Lagrangian fibrations and special Kähler geometry

2021 ◽  
Author(s):  
Ljudmila Kamenova ◽  
Misha Verbitsky
Keyword(s):  
Symplectic Manifolds ◽  
Kahler Geometry

Constructing symplectic manifolds

2017 ◽  
Author(s):  
Dusa McDuff ◽  
Dietmar Salamon
Keyword(s):  
Final Section ◽  
Symplectic Manifolds ◽  
Homotopy Equivalence ◽  
Codimension Two ◽  
Open Manifolds ◽  
Connected Sums ◽  
Symplectic Forms ◽  
Ambient Manifold ◽  
Blowing Up ◽  
Four Manifolds

This chapter examines various ways to construct symplectic manifolds and submanifolds. It begins by studying blowing up and down in both the complex and the symplectic contexts. The next section is devoted to a discussion of fibre connected sums and describes Gompf’s construction of symplectic four-manifolds with arbitrary fundamental group. The chapter also contains an exposition of Gromov’s telescope construction, which shows that for open manifolds the h-principle rules and the inclusion of the space of symplectic forms into the space of nondegenerate 2-forms is a homotopy equivalence. The final section outlines Donaldson’s construction of codimension two symplectic submanifolds and explains the associated decompositions of the ambient manifold.

scholarly journals Deformation classes in generalized Kähler geometry

2020 ◽  
Vol 7 (1) ◽  
pp. 241-256
Author(s):  
Matthew Gibson ◽  
Jeffrey Streets
Keyword(s):  
Symmetry Group ◽  
Ricci Flow ◽  
Kahler Geometry ◽  
Poisson Tensor ◽  
Natural Extensions ◽  
Generalized Kähler Geometry ◽  
Kähler Structures

AbstractWe describe natural deformation classes of generalized Kähler structures using the Courant symmetry group, which determine natural extensions of the notions of Kähler class and Kähler cone to generalized Kähler geometry. We show that the generalized Kähler-Ricci flow preserves this generalized Kähler cone, and the underlying real Poisson tensor.

scholarly journals Hamilton–Jacobi formalism on locally conformally symplectic manifolds

2021 ◽  
Vol 62 (3) ◽  
pp. 033506
Author(s):  
Oğul Esen ◽  
Manuel de León ◽  
Cristina Sardón ◽  
Marcin Zajşc
Keyword(s):  
Symplectic Manifolds ◽  
Jacobi Formalism ◽  
Locally Conformally Symplectic

scholarly journals Poisson structures of near-symplectic manifolds and their cohomology

2021 ◽  
Vol 62 (3) ◽  
pp. 033513
Author(s):  
Panagiotis Batakidis ◽  
Ramón Vera
Keyword(s):  
Symplectic Manifolds ◽  
Poisson Structures

scholarly journals NON-SYMPLECTIC INVOLUTIONS ON MANIFOLDS OF -TYPE

2020 ◽  
pp. 1-25
Author(s):  
CHIARA CAMERE ◽  
ALBERTO CATTANEO ◽  
ANDREA CATTANEO
Keyword(s):  
Moduli Spaces ◽  
Quadratic Forms ◽  
Symplectic Manifolds ◽  
Hilbert Schemes ◽  
Small Rank ◽  
Twisted Sheaves ◽  
Formula Type

We study irreducible holomorphic symplectic manifolds deformation equivalent to Hilbert schemes of points on a $K3$ surface and admitting a non-symplectic involution. We classify the possible discriminant quadratic forms of the invariant and coinvariant lattice for the action of the involution on cohomology and explicitly describe the lattices in the cases where the invariant lattice has small rank. We also give a modular description of all $d$ -dimensional families of manifolds of $K3^{[n]}$ -type with a non-symplectic involution for $d\geqslant 19$ and $n\leqslant 5$ and provide examples arising as moduli spaces of twisted sheaves on a $K3$ surface.

scholarly journals An obstruction to quantizing compact symplectic manifolds

1999 ◽  
Vol 128 (1) ◽  
pp. 237-243 ◽  
Author(s):  
Mark J. Gotay ◽  
Janusz Grabowski ◽  
Hendrik B. Grundling
Keyword(s):  
Symplectic Manifolds

Some Properties of Symplectic Manifolds S on the Projective Tangent Bundle PTM

2011 ◽  
Vol 187 ◽  
pp. 483-486
Author(s):  
Yong He ◽  
Xiao Ying Lu ◽  
Wei Na Lu
Keyword(s):  
Vector Field ◽  
Symplectic Manifold ◽  
Tangent Bundle ◽  
Fiber Bundle ◽  
Symplectic Manifolds ◽  
Lie Derivative ◽  
The Relationship

In this paper, we show the relationship between 2-form of the two projective tangent bundle and the relationship between 2-form on projective tangent bundle and 1-form on by using the theory of fiber bundle and the properties of symplectic manifold of the projective tangent bundle . Moreover, we derived a simpler formula of Lie derivative of a special vector field, which is on the projective tangent bundle.

Examples for obstructions to action-angle coordinates

1988 ◽  
Vol 110 (1-2) ◽  
pp. 27-30 ◽  
Author(s):  
Larry M. Bates
Keyword(s):  
Global Existence ◽  
Symplectic Manifolds ◽  
Torus Bundles

SynopsisWe give examples of symplectic manifolds which are also non-trivial principal torus-bundles with Lagrangian fibres. These bundles are examples of spaces with an obstruction to the global existence of action-angle variables.

Collective coordinates on symplectic manifolds

1982 ◽  
Vol 52 (1) ◽  
pp. 641-647 ◽  
Author(s):  
A. V. Razumov ◽  
A. Yu. Taranov
Keyword(s):  
Symplectic Manifolds ◽  
Collective Coordinates
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