Slice regular functions and orthogonal complex structures over ${\mathbb{R}}^8$

Abstract

This work looks at the theory of octonionic slice regular functions through the lens of differential topology. It proves a full-fledged version of the Open Mapping Theorem for octonionic slice regular functions. Moreover, it opens the path for a possible use of slice regular functions in the study of almost-complex structures in eight dimensions.

arXiv comment35 pages, published online in the Journal of Noncommutative Geometry

References in corpus (6)

• Slice regular functions on real alternative algebras
• Twistor transforms of quaternionic functions and orthogonal complex structures
• Singularities of slice regular functions over real alternative *-algebras
• Power and spherical series over real alternative *-algebras
• Twistor geometry and warped product orthogonal complex structures
• Orthogonal complex structures on domains in R^4

Cited by in corpus (2)

• Cauchy-Riemann operators and local slice analysis over real alternative algebras
• Slice conformality and Riemann manifolds on quaternions and octonions