Address:
Department of Theoretical Physics and Astrophysics, Faculty of Science, Masaryk University, 611 37 Brno, Czech Republic
Department of Mathematics and Statistics, Faculty of Science, Masaryk University, 611 37 Brno, Czech Republic and Angevin Laboratory of Mathematical Research - UMR CNRS 6093, University of Angers, 2 Boulevard Lavoisier, 49045, Angers CEDEX 0, France
E-mail: r.suchanek.r@gmail.com
Abstract: 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.
AMSclassification: primary 53B20; secondary 83C15.
Keywords: Hessian structure, Lychagin-Rubtsov metric, Monge-Ampère structure, Monge-Ampère equation, Plücker embedding.
DOI: 10.5817/AM2022-5-329