Connections on contact manifolds and contact twistor space

2010 ◽  
Vol 178 (1) ◽  
pp. 253-267 ◽  
Author(s):  
Luigi Vezzoni
Keyword(s):  
Twistor Space ◽  
Contact Manifolds

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 The Adjunction Inequality for Weyl-Harmonic Maps

2020 ◽  
Vol 7 (1) ◽  
pp. 129-140
Author(s):  
Robert Ream
Keyword(s):  
Minimal Surfaces ◽  
Twistor Space ◽  
Harmonic Maps ◽  
Holomorphic Curves ◽  
Weyl Connection ◽  
Almost Kähler ◽  
Conformal Manifolds

AbstractIn this paper we study an analog of minimal surfaces called Weyl-minimal surfaces in conformal manifolds with a Weyl connection (M4, c, D). We show that there is an Eells-Salamon type correspondence between nonvertical 𝒥-holomorphic curves in the weightless twistor space and branched Weyl-minimal surfaces. When (M, c, J) is conformally almost-Hermitian, there is a canonical Weyl connection. We show that for the canonical Weyl connection, branched Weyl-minimal surfaces satisfy the adjunction inequality\chi \left( {{T_f}\sum } \right) + \chi \left( {{N_f}\sum } \right) \le \pm {c_1}\left( {f*{T^{\left( {1,0} \right)}}M} \right).The ±J-holomorphic curves are automatically Weyl-minimal and satisfy the corresponding equality. These results generalize results of Eells-Salamon and Webster for minimal surfaces in Kähler 4-manifolds as well as their extension to almost-Kähler 4-manifolds by Chen-Tian, Ville, and Ma.

scholarly journals Prolongation on contact manifolds

2011 ◽  
Vol 60 (5) ◽  
pp. 1425-1486 ◽  
Author(s):  
Michael Eastwood ◽  
A. Rod Gover
Keyword(s):  
Contact Manifolds

scholarly journals The Weyl double copy from twistor space

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Erick Chacón ◽  
Silvia Nagy ◽  
Chris D. White
Keyword(s):  
Exact Solutions ◽  
Twistor Space ◽  
Current Form ◽  
New Formalism ◽  
Petrov Types ◽  
Gravity Theories ◽  
Double Copy

Abstract The Weyl double copy is a procedure for relating exact solutions in biadjoint scalar, gauge and gravity theories, and relates fields in spacetime directly. Where this procedure comes from, and how general it is, have until recently remained mysterious. In this paper, we show how the current form and scope of the Weyl double copy can be derived from a certain procedure in twistor space. The new formalism shows that the Weyl double copy is more general than previously thought, applying in particular to gravity solutions with arbitrary Petrov types. We comment on how to obtain anti-self-dual as well as self-dual fields, and clarify some conceptual issues in the twistor approach.

scholarly journals Inherited twistor-space structure of gravity amplitudes

2005 ◽  
Vol 2005 (05) ◽  
pp. 056-056 ◽  
Author(s):  
Zvi Bern ◽  
Niels Emil Jannik Bjerrum-Bohr ◽  
David C Dunbar
Keyword(s):  
Twistor Space ◽  
Space Structure

On the non-regularity of tangent sphere bundles

1978 ◽  
Vol 82 (1-2) ◽  
pp. 13-17 ◽  
Author(s):  
David E. Blair
Keyword(s):  
Riemannian Manifold ◽  
Large Class ◽  
Constant Curvature ◽  
Positive Constant ◽  
Contact Structure ◽  
Compact Riemannian Manifold ◽  
Contact Structures ◽  
Sphere Bundle ◽  
Contact Manifolds ◽  
Tangent Sphere

SynopsisClassically the tangent sphere bundles have formed a large class of contact manifolds; their contact structures are not in general regular, however. Specifically we prove that the natural contact structure on the tangent sphere bundle of a compact Riemannian manifold of non-positive constant curvature is not regular.

scholarly journals Cartan structures on contact manifolds

1981 ◽  
Vol 266 (2) ◽  
pp. 583-583 ◽  
Author(s):  
G. Burdet ◽  
M. Perrin
Keyword(s):  
Contact Manifolds
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