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Pseudo-Riemannian and Hessian geometry related to Monge-Ampère structures. (English) Zbl 07655751

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.

MSC:

53B20 Local Riemannian geometry
83C15 Exact solutions to problems in general relativity and gravitational theory
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