scholarly journals Integrable Complex Structures on Twistor Spaces

2019 ◽  
Vol 70 (3) ◽  
pp. 937-963
Author(s):  
Steven Gindi
Keyword(s):  
Twistor Space ◽  
Complex Structures ◽  
Complex Manifolds ◽  
Twistor Spaces

Abstract We introduce integrable complex structures on twistor spaces fibered over complex manifolds. We then show, in particular, that the twistor spaces associated with generalized Kahler, SKT and strong HKT manifolds all naturally admit complex structures. Moreover, in the strong HKT case, we construct a metric and three compatible complex structures on the twistor space that have equal torsions.

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 Compatible complex structures on twistor space

2011 ◽  
Vol 61 (6) ◽  
pp. 2219-2248 ◽  
Author(s):  
Guillaume Deschamps
Keyword(s):  
Twistor Space ◽  
Complex Structures

scholarly journals Quaternionic-like manifolds and homogeneous twistor spaces

2016 ◽  
Vol 472 (2196) ◽  
pp. 20160598
Author(s):  
Radu Pantilie
Keyword(s):  
Complex Manifolds ◽  
Twistor Spaces ◽  
Adequate Level ◽  
Homogeneous Complex ◽  
Quaternionic Manifold ◽  
Quaternionic Geometry ◽  
Real Analytic ◽  
Quaternionic Manifolds

Motivated by the quaternionic geometry corresponding to the homogeneous complex manifolds endowed with (holomorphically) embedded spheres, we introduce and initiate the study of the ‘quaternionic-like manifolds’. These contain, as particular subclasses, the CR quaternionic and the ρ -quaternionic manifolds. Moreover, the notion of ‘heaven space’ finds its adequate level of generality in this setting: (essentially) any real analytic quaternionic-like manifold admits a (germ) unique heaven space, which is a ρ -quaternionic manifold. We, also, give a natural construction of homogeneous complex manifolds endowed with embedded spheres, thus, emphasizing the abundance of the quaternionic-like manifolds.

scholarly journals Energy of sections of the Deligne–Hitchin twistor space

2020 ◽  
Author(s):  
Florian Beck ◽  
Sebastian Heller ◽  
Markus Röser
Keyword(s):  
Moduli Space ◽  
Compact Riemann Surface ◽  
Twistor Space ◽  
Harmonic Maps ◽  
Energy Functional ◽  
Conformal Map ◽  
Twistor Spaces ◽  
Holomorphic Sections ◽  
Meromorphic Connection ◽  
Willmore Energy

Abstract We study a natural functional on the space of holomorphic sections of the Deligne–Hitchin moduli space of a compact Riemann surface, generalizing the energy of equivariant harmonic maps corresponding to twistor lines. We show that the energy is the residue of the pull-back along the section of a natural meromorphic connection on the hyperholomorphic line bundle recently constructed by Hitchin. As a byproduct, we show the existence of a hyper-Kähler potentials for new components of real holomorphic sections of twistor spaces of hyper-Kähler manifolds with rotating $$S^1$$ S 1 -action. Additionally, we prove that for a certain class of real holomorphic sections of the Deligne–Hitchin moduli space, the energy functional is basically given by the Willmore energy of corresponding equivariant conformal map to the 3-sphere. As an application we use the functional to distinguish new components of real holomorphic sections of the Deligne–Hitchin moduli space from the space of twistor lines.

scholarly journals Complex Multiplication in Twistor Spaces

2020 ◽  
Author(s):  
D Huybrechts
Keyword(s):  
Twistor Space ◽  
Complex Multiplication ◽  
K3 Surface ◽  
Twistor Spaces ◽  
Arithmetic Properties ◽  
Twistor Construction

Abstract Despite the transcendental nature of the twistor construction, the algebraic fibres of the twistor space of a K3 surface share certain arithmetic properties. We prove that for a polarised K3 surface with complex multiplication, all algebraic fibres of its twistor space away from the equator have complex multiplication as well.

Twistors and fields with sources on worldlines

1985 ◽  
Vol 397 (1812) ◽  
pp. 143-155 ◽  
Keyword(s):  
Minkowski Space ◽  
Twistor Space ◽  
Rest Mass ◽  
Double Cover ◽  
Ruled Surface ◽  
Hausdorff Spaces ◽  
Twistor Spaces ◽  
Non Hausdorff Spaces ◽  
Massless Fields

It is shown that zero-rest-mass fields with sources on an analytic worldline are naturally defined on a double cover of some region of Minkowski space. Twistor spaces are constructed that correspond to such regions and these turn out to be non-Hausdorff spaces, obtained by identifying two copies of regions in ordinary twistor space, except on a ruled surface that corresponds to the worldline. It is shown that cohomology classes on the twistor space corresponds to sourced fields on Minkowski space, thus extending the twistor descrip­tion of massless fields.

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