Twistor geometry and warped product orthogonal complex structures
Differential Geometry
2019-12-19 v1 Algebraic Geometry
Abstract
The twistor space of the sphere S^{2n} is an isotropic Grassmannian that fibers over S^{2n}. An orthogonal complex structure on a subdomain of S^{2n} (a complex structure compatible with the round metric) determines a section of this fibration with holomorphic image. In this paper, we use this correspondence to prove that any finite energy orthogonal complex structure on R^6 must be of a special warped product form, and we also prove that any orthogonal complex structure on R^{2n} that is asymptotically constant must itself be constant. We will also give examples defined on R^{2n} which have infinite energy, and examples of non-standard orthogonal complex structures on flat tori in complex dimension three and greater.
Cite
@article{arxiv.0905.3662,
title = {Twistor geometry and warped product orthogonal complex structures},
author = {Lev Borisov and Simon Salamon and Jeff Viaclovsky},
journal= {arXiv preprint arXiv:0905.3662},
year = {2019}
}
Comments
39 pages