Generalized Geometries Constructed from Differential Forms on Cotangent Bundle
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.
Keywords
Cite
@article{arxiv.2305.04591,
title = {Generalized Geometries Constructed from Differential Forms on Cotangent Bundle},
author = {Radek Suchánek},
journal= {arXiv preprint arXiv:2305.04591},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:2305.03580