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Pseudo-Riemannian and Hessian Geometry Related to Monge-Ampère Structures (2305.03579v1)
Published 5 May 2023 in math.DG, math-ph, and math.MP
Abstract: We study properties of pseudo-Riemannian metrics corresponding to Monge-Amp`ere structures on four-dimensional $T*M$. We describe a family of Ricci flat solutions, which are parametrized by six coefficients satisfying the Pl\"ucker embedding equation. We also focus on pullbacks of the pseudo-metrics on two-dimensional $M$ and describe the corresponding Hessian structures.
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