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Keywords:
Hessian structure; Lychagin-Rubtsov metric; Monge-Ampère structure; Monge-Ampère equation; Plücker embedding
Hessian structure; Lychagin-Rubtsov metric; Monge-Ampère structure; Monge-Ampère equation; Plücker embedding
Summary:
We study properties of pseudo-Riemannian metrics corresponding to Monge-Ampère structures on four dimensional $T^*M$. We describe a family of Ricci flat solutions, which are parametrized by six coefficients satisfying the Plücker 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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