Pseudo-Riemannian and Hessian geometry related to Monge-Ampère structures

S. Hronek; R. Suchánek

Archivum Mathematicum (2022)

  • Volume: 058, Issue: 5, page 329-338
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Hronek, S., and Suchánek, R.. "Pseudo-Riemannian and Hessian geometry related to Monge-Ampère structures." Archivum Mathematicum 058.5 (2022): 329-338. <http://eudml.org/doc/298918>.

@article{Hronek2022,
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.},
author = {Hronek, S., Suchánek, R.},
journal = {Archivum Mathematicum},
keywords = {Hessian structure; Lychagin-Rubtsov metric; Monge-Ampère structure; Monge-Ampère equation; Plücker embedding},
language = {eng},
number = {5},
pages = {329-338},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Pseudo-Riemannian and Hessian geometry related to Monge-Ampère structures},
url = {http://eudml.org/doc/298918},
volume = {058},
year = {2022},
}

TY - JOUR
AU - Hronek, S.
AU - Suchánek, R.
TI - Pseudo-Riemannian and Hessian geometry related to Monge-Ampère structures
JO - Archivum Mathematicum
PY - 2022
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 058
IS - 5
SP - 329
EP - 338
AB - 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.
LA - eng
KW - Hessian structure; Lychagin-Rubtsov metric; Monge-Ampère structure; Monge-Ampère equation; Plücker embedding
UR - http://eudml.org/doc/298918
ER -

References

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