Dennis The, On 4D Split-conformal Structures with G₂-symmetric Twistor Distribution

In their 2013 article, An & Nurowski considered two surfaces rolling on each other without twisting or slipping, and defined a twistor distribution (on the space of all real totally null self-dual 2-planes) for the associated 4D split-signature conformal structure. If this split-conformal structure is not anti-self dual, then the twistor distribution is a (2,3,5)-distribution, and An-Nurowski identified interesting rolling examples where it achieves maximal, i.e. G2, symmetry. Relaxing the rolling assumption, a similar construction can be made for any 4D split-conformal structure, and my talk will discuss a broader classification of examples where such exceptional symmetry for the twistor distribution is achieved. (Joint work with Pawel Nurowski & Katja Sagerschnig.)