2023/05/08 by Radek Suchánek, Suchánek, Radek
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2305.04591
openalex publication_date 2023/05/08 · openalex created_date 2023/05/10 · openalex updated_date 2026/07/28
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.