Abstract
AbstractIn this paper, we study the twistor space of an oriented Riemannian 4‐manifold using the moving frame approach, focusing, in particular, on the Einstein, non‐self‐dual setting. We prove that any general first‐order linear condition on the almost complex structures of forces the underlying manifold to be self‐dual, also recovering most of the known related rigidity results. Thus, we are naturally lead to consider first‐order quadratic conditions, showing that the Atiyah–Hitchin–Singer almost Hermitian twistor space of an Einstein 4‐manifold bears a resemblance, in a suitable sense, to a nearly Kähler manifold.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
