scholarly journals Optimal Symplectic Connections on Holomorphic Submersions

2020 ◽  
Author(s):  
Ruadhaí Dervan ◽  
Lars Martin Sektnan
Keyword(s):  
Symplectic Connections

SYMPLECTIC CONNECTIONS AND EXOTIC HOLONOMY

1998 ◽  
Vol 09 (01) ◽  
pp. 47-61 ◽  
Author(s):  
QUO-SHIN CHI
Keyword(s):  
Symplectic Connections ◽  
Torsion Free

We show that exotic holonomies arise naturally from torsion-free sympletic connections.

scholarly journals SYMPLECTIC CONNECTIONS

2006 ◽  
Vol 03 (03) ◽  
pp. 375-420 ◽  
Author(s):  
PIERRE BIELIAVSKY ◽  
MICHEL CAHEN ◽  
SIMONE GUTT ◽  
JOHN RAWNSLEY ◽  
LORENZ SCHWACHHÖFER
Keyword(s):  
Variational Principle ◽  
Critical Points ◽  
Ricci Tensor ◽  
Symmetric Spaces ◽  
Complex Geometry ◽  
Ricci Flat ◽  
Symplectic Connections

This article is an overview of the results obtained in recent years on symplectic connections. We present what is known about preferred connections (critical points of a variational principle). The class of Ricci-type connections (for which the curvature is entirely determined by the Ricci tensor) is described in detail, as well as its far-reaching generalization to special connections. A twistorial construction shows a relation between Ricci-type connections and complex geometry. We give a construction of Ricci-flat symplectic connections. We end up by presenting, through an explicit example, an approach to non-commutative symplectic symmetric spaces.

scholarly journals Remarks on Symplectic Connections

2006 ◽  
Vol 78 (3) ◽  
pp. 307-328 ◽  
Author(s):  
Simone Gutt
Keyword(s):  
Symplectic Connections

Special Symplectic Connections and Poisson Geometry

2004 ◽  
Vol 69 (1-3) ◽  
pp. 115-137 ◽  
Author(s):  
Michel Cahen ◽  
LORENZ J. SCHWACHH�FER
Keyword(s):  
Poisson Geometry ◽  
Symplectic Connections
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