Geodesic
Pseudo-Riemannian and Hessian geometry related to Monge-Ampère structures
Archivum mathematicum, Tome 58 (2022) no. 5, pp. 329-338 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.5817/AM2022-5-329
Classification : 53B20, 83C15
Keywords: Hessian structure; Lychagin-Rubtsov metric; Monge-Ampère structure; Monge-Ampère equation; Plücker embedding 
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     title = {Pseudo-Riemannian and {Hessian} geometry related to {Monge-Amp\`ere} structures},
     journal = {Archivum mathematicum},
     pages = {329--338},
     year = {2022},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2022-5-329/}
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Hronek, S.; Suchánek, R. Pseudo-Riemannian and Hessian geometry related to Monge-Ampère structures. Archivum mathematicum, Tome 58 (2022) no. 5, pp. 329-338. doi: 10.5817/AM2022-5-329

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