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arXiv · 2305.04591

Generalized Geometries Constructed from Differential Forms on Cotangent Bundle

Radek Suchánek
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Abstract

We investigate the landscape of generalized geometries that can be derived from Monge-Amp\`ere 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-Amp\`ere structures and other related geometric objects, such as complex structures. We demonstrate that, under certain assumptions, non-degenerate Monge-Amp\`ere structures give rise to quadric surfaces of generalized almost geometries. Additionally, we discuss the link between Monge-Amp\`ere structures and Monge-Amp\`ere equations within this framework.

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Radek Suchánek. 2023-05-08. Generalized Geometries Constructed from Differential Forms on Cotangent Bundle. https://arxiv.org/abs/2305.04591

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