Elementary twistor theory for harmonic maps

2001 ◽  
pp. 52-62
Author(s):  
Frédéric Hélein
Keyword(s):  
Harmonic Maps ◽  
Twistor Theory

An Introduction to Twistor Theory

1994 ◽  
Author(s):  
S. A. Huggett ◽  
K. P. Tod
Keyword(s):  
Twistor Theory

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 Philosophical Aspects of Astrobiology Revisited

Philosophies ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 55
Author(s):  
Rainer E. Zimmermann
Keyword(s):  
Dynamical Systems ◽  
First Principles ◽  
Special Form ◽  
Mathematical Representation ◽  
Dynamical Structure ◽  
Twistor Theory ◽  
Fundamental Physics ◽  
Physical Universe ◽  
The World ◽  
Traditional Sense

Given the idea that Life as we know it is nothing but a special form of a generically underlying dynamical structure within the physical Universe, we try to introduce a concept of Life that is not only derived from first principles of fundamental physics, but also metaphysically based on philosophical assumptions about the foundations of the world. After clarifying the terminology somewhat, especially with a view to differentiating reality from modality, we give an example for a mathematical representation of what the substance of reality (in the traditional sense of metaphysics) could actually mean today, discussing twistor theory as an example. We then concentrate on the points of structural emergence by discussing the emergence of dynamical systems and of Life as we know it, respectively. Some further consequences as they relate to meaning are discussed in the end.

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