Almost complex structures

2017 ◽  
Author(s):  
Dusa McDuff ◽  
Dietmar Salamon
Keyword(s):  
Complex Projective Space ◽  
Betti Numbers ◽  
Symplectic Manifolds ◽  
Holomorphic Curves ◽  
Complex Structures ◽  
Chern Classes ◽  
Complex Dimension ◽  
Almost Complex Structures ◽  
Almost Complex ◽  
Complex Projective

The chapter begins with a general discussion of almost complex structures on symplectic manifolds and then addresses the problem of integrability. Subsequent sections discuss a variety of examples of Kähler manifolds, in particular those of complex dimension two, and show how to compute the Chern classes and Betti numbers of hypersurfaces in complex projective space. The last section is a brief introduction to the theory of J-holomorphic curves.

scholarly journals Symplectic and Contact Geometry with Complex Manifolds

2019 ◽  
Vol 39 ◽  
pp. 119-126
Author(s):  
AKM Nazimuddin ◽  
Md Showkat Ali
Keyword(s):  
Riemannian Manifolds ◽  
Symplectic Geometry ◽  
Contact Geometry ◽  
Symplectic Manifolds ◽  
Complex Structures ◽  
Contact Manifolds ◽  
Almost Complex Structures ◽  
Almost Complex ◽  
Real Submanifold ◽  
Complex Symplectic

In this paper, we discuss about almost complex structures and complex structures on Riemannian manifolds, symplectic manifolds and contact manifolds. We have also shown a special comparison between complex symplectic geometry and complex contact geometry. Also, the existence of a complex submanifold of n-dimensional complex manifold which intersects a real submanifold GANIT J. Bangladesh Math. Soc.Vol. 39 (2019) 119-126

scholarly journals Berezin–Toeplitz Quantization and the Least Unsharpness Principle

2020 ◽  
Author(s):  
Louis Ioos ◽  
David Kazhdan ◽  
Leonid Polterovich
Keyword(s):  
Symplectic Manifolds ◽  
Complex Structures ◽  
Almost Complex Structures ◽  
Almost Complex

Abstract We show that compatible almost-complex structures on symplectic manifolds correspond to optimal positive quantizations.

ON NORMAL CONTACT PAIRS

2010 ◽  
Vol 21 (06) ◽  
pp. 737-754 ◽  
Author(s):  
GIANLUCA BANDE ◽  
AMINE HADJAR
Keyword(s):  
Symplectic Manifolds ◽  
Contact Pair ◽  
Complex Structures ◽  
Complex Manifolds ◽  
Contact Manifolds ◽  
Normal Contact ◽  
New Methods ◽  
Almost Complex Structures ◽  
Almost Complex

We consider manifolds endowed with a contact pair structure. To such a structure are naturally associated two almost complex structures. If they are both integrable, we call the structure a normal contact pair. We generalize Morimoto's Theorem on the product of almost contact manifolds to flat bundles. We construct some examples on Boothby–Wang fibrations over contact-symplectic manifolds. In particular, these results give new methods to construct complex manifolds.

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