Generalized Geometries Constructed from Differential Forms on Cotangent Bundle

Abstract

We investigate the landscape of generalized geometries that can be derived from Monge-Ampère structures. Instead of following the approaches of Banos, Roubtsov, Kosmann-Schwarzbach, and others, we take a new path inspired by the results of Hu, Moraru, and Svoboda. We construct a large family of new generalized almost geometries derived from non-degenerate 2D symplectic Monge-Ampère structures and other related geometric objects, such as complex structures. We demonstrate that, under certain assumptions, non-degenerate Monge-Ampère structures give rise to quadric surfaces of generalized almost geometries. Additionally, we discuss the link between Monge-Ampère structures and Monge-Ampère equations within this framework.

arXiv admin note: text overlap with arXiv:2305.03580