Twistor transforms of quaternionic functions and orthogonal complex structures

Abstract

The theory of slice regular functions of a quaternion variable is applied to the study of orthogonal complex structures on domains Ω of R^4. When Ω is a symmetric slice domain, the twistor transform of such a function is a holomorphic curve in the Klein quadric. The case in which Ω is the complement of a parabola is studied in detail and described by a rational quartic surface in the twistor space CP^3.

Some explanation added in section 1, other minor amendments and reformatting; to appear in JEMS

References in corpus (1)

• Orthogonal complex structures on domains in R^4

Cited by in corpus (30)

• The algebra of slice functions
• Geometric function theory over quaternionic slice domains
• Twistor interpretation of slice regular functions
• Slice-Polynomial Functions and Twistor Geometry of Ruled Surfaces in ${\mathbb{CP}}^3$
• Slice-quaternionic Hopf surfaces
• Twistor lines on cubic surfaces
• On a class of orientation-preserving maps of ${\mathbb{R}}^4$
• On the real differential of a slice regular function
• Twistors and Bi-Hermitian Surfaces of Non-Kähler Type
• S-regular functions which preserve a complex slice
• Landau's theorem for slice regular functions on the quaternionic unit ball
• The Growth and Distortion Theorems for Slice Monogenic Functions
• Twistor geometry of the Flag manifold
• Twistor lines on algebraic surfaces
• Slice regular functions and orthogonal complex structures over ${\mathbb{R}}^8$
• Algebraic surfaces with infinitely many twistor lines
• A new approach to slice analysis via slice topology
• Three Topological Results on the Twistor Discriminant Locus in the 4-Sphere
• Some notions of subharmonicity over the quaternions
• The twistor space of a real associative algebra: incidence geometry, semisimple classification and slice-regular functions
• Slice regular functions as covering maps and global $\star$-roots
• On two Bloch type theorems for quaternionic slice regular functions
• A direct approach to quaternionic manifolds
• Slice Dirac operator over octonions
• Riemann slice-domains over quaternions I
• The Mittag-Leffler Theorem for regular functions of a quaternionic variable
• Weak slice regular functions on the $n$-dimensional quadratic cone of octonions
• On geometric aspects of quaternionic and octonionic slice regular functions
• Ideals of regular functions of a quaternionic variable
• Julia theory for slice regular functions