Between generalized complex and Poisson geometry

10.33540/793 ◽  
2021 ◽  
Author(s):  
◽  
Geraldo Arend Witte
Keyword(s):  
Poisson Geometry ◽  
Generalized Complex

scholarly journals The Local Structure of Generalized Contact Bundles

2019 ◽  
Vol 2020 (20) ◽  
pp. 6871-6925 ◽  
Author(s):  
Jonas Schnitzer ◽  
Luca Vitagliano
Keyword(s):  
Line Bundle ◽  
Symplectic Manifold ◽  
Complex Manifold ◽  
Local Structure ◽  
Complex Structure ◽  
Regular Point ◽  
Poisson Geometry ◽  
Splitting Theorem ◽  
Complex Manifolds ◽  
Generalized Complex

Abstract Generalized contact bundles are odd-dimensional analogues of generalized complex manifolds. They have been introduced recently and very little is known about them. In this paper we study their local structure. Specifically, we prove a local splitting theorem similar to those appearing in Poisson geometry. In particular, in a neighborhood of a regular point, a generalized contact bundle is either the product of a contact and a complex manifold or the product of a symplectic manifold and a manifold equipped with an integrable complex structure on the gauge algebroid of the trivial line bundle.

scholarly journals Simultaneous deformations and Poisson geometry

2015 ◽  
Vol 151 (9) ◽  
pp. 1763-1790 ◽  
Author(s):  
Yaël Frégier ◽  
Marco Zambon
Keyword(s):  
Complex Geometry ◽  
Poisson Manifolds ◽  
Poisson Geometry ◽  
Complex Structures ◽  
Poisson Structures ◽  
Coisotropic Submanifolds ◽  
Generalized Complex ◽  
Derived Bracket

We consider the problem of deforming simultaneously a pair of given structures. We show that such deformations are governed by an $L_{\infty }$-algebra, which we construct explicitly. Our machinery is based on Voronov’s derived bracket construction. In this paper we consider only geometric applications, including deformations of coisotropic submanifolds in Poisson manifolds, of twisted Poisson structures, and of complex structures within generalized complex geometry. These applications cannot be, to our knowledge, obtained by other methods such as operad theory.

Geometry and Physics: Volume II

2018 ◽  
Keyword(s):  
Moduli Spaces ◽  
Mirror Symmetry ◽  
Geometric Analysis ◽  
Mathematical Physics ◽  
Poisson Geometry ◽  
Special Holonomy ◽  
Low Dimensional Topology ◽  
Generalized Complex Structures ◽  
Wide Range ◽  
Low Dimensional

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and Savilian Professor of Geometry at Oxford. The proceedings contain twenty-nine articles, including three by Fields medallists (Donaldson, Mori and Yau). The articles cover a wide range of topics in geometry and mathematical physics, including the following: Riemannian geometry, geometric analysis, special holonomy, integrable systems, dynamical systems, generalized complex structures, symplectic and Poisson geometry, low-dimensional topology, algebraic geometry, moduli spaces, Higgs bundles, geometric Langlands programme, mirror symmetry and string theory. These volumes will be of interest to researchers and graduate students both in geometry and mathematical physics.

Towards creating a generalized complex event processing operator using FlinkCEP

2021 ◽  
Author(s):  
Eleni Kougioumtzi ◽  
Antonios Kontaxakis ◽  
Antonios Deligiannakis ◽  
Yannis Kotidis
Keyword(s):  
Complex Event Processing ◽  
Event Processing ◽  
Generalized Complex

scholarly journals Invariant generalized complex geometry on maximal flag manifolds and their moduli

2021 ◽  
pp. 104108
Author(s):  
Elizabeth Gasparim ◽  
Fabricio Valencia ◽  
Carlos Varea
Keyword(s):  
Complex Geometry ◽  
Flag Manifolds ◽  
Generalized Complex

scholarly journals Generalized almost even-Clifford manifolds and their twistor spaces

2021 ◽  
Vol 8 (1) ◽  
pp. 96-124
Author(s):  
Luis Fernando Hernández-Moguel ◽  
Rafael Herrera
Keyword(s):  
Twistor Space ◽  
Complex Structure ◽  
Twistor Spaces ◽  
Recent Interest ◽  
Generalized Complex Structure ◽  
Generalized Complex ◽  
Space Construction ◽  
Clifford Structures

Abstract Motivated by the recent interest in even-Clifford structures and in generalized complex and quaternionic geometries, we introduce the notion of generalized almost even-Clifford structure. We generalize the Arizmendi-Hadfield twistor space construction on even-Clifford manifolds to this setting and show that such a twistor space admits a generalized complex structure under certain conditions.

scholarly journals Hans Duistermaat’s contributions to Poisson geometry

2011 ◽  
Vol 42 (4) ◽  
pp. 783-803 ◽  
Author(s):  
Reyer Sjamaar
Keyword(s):  
Poisson Geometry

scholarly journals Gaugino mass term for D-branes and Generalized Complex Geometry

2020 ◽  
Vol 2020 (6) ◽  
Author(s):  
Mariana Graña ◽  
Nicolás Kovensky ◽  
Ander Retolaza
Keyword(s):  
Complex Geometry ◽  
Mass Term ◽  
Gaugino Mass ◽  
Generalized Complex

scholarly journals Left and right centers in quasi-Poisson geometry of moduli spaces

2015 ◽  
Vol 279 ◽  
pp. 263-290 ◽  
Author(s):  
Pavol Ševera
Keyword(s):  
Moduli Spaces ◽  
Poisson Geometry ◽  
Left And Right

scholarly journals CR-warped product submanifolds of a generalized complex space form

2017 ◽  
Vol 4 (1) ◽  
pp. 1306153
Author(s):  
Meraj Ali Khan ◽  
Amira A. Ishan ◽  
Hari M. Srivastava
Keyword(s):  
Warped Product ◽  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Generalized Complex
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