Twistor space of a generalized quaternionic manifold

We extend T. Y. Thomas’s approach to projective structures, over the complex analytic category, by involving the $\unicode[STIX]{x1D70C}$-connections. This way, a better control of projective flatness is obtained and, consequently, we have, for example, the following application: if the twistor space of a quaternionic manifold $P$ is endowed with a complex projective structure then $P$ can be locally identified, through quaternionic diffeomorphisms, with the quaternionic projective space.

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Holomorphic vertical line bundle of the twistor space over a quaternionic manifold

Journal of the Mathematical Society of Japan ◽

10.2969/jmsj/05230485 ◽

2000 ◽

Vol 52 (3) ◽

pp. 485-499 ◽

Cited By ~ 1

Author(s):

Toshimasa KOBAYASHI

Keyword(s):

Line Bundle ◽

Twistor Space ◽

Vertical Line ◽

Quaternionic Manifold

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Generalized almost even-Clifford manifolds and their twistor spaces

Complex Manifolds ◽

10.1515/coma-2020-0108 ◽

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.

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The Adjunction Inequality for Weyl-Harmonic Maps

Complex Manifolds ◽

10.1515/coma-2020-0007 ◽

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.

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Higher-spin initial data in twistor space with complex stargenvalues

Journal of High Energy Physics ◽

10.1007/jhep06(2020)066 ◽

2020 ◽

Vol 2020 (6) ◽

Author(s):

Yihao Yin

Keyword(s):

Initial Data ◽

Twistor Space ◽

Higher Spin

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The Weyl double copy from twistor space

Journal of High Energy Physics ◽

10.1007/jhep05(2021)239 ◽

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.

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