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Riemannian F-Manifolds, Bi-Flat F-Manifolds, and Flat Pencils of Metrics. / Arsie, Alessandro; Buryak, Alexandr; Lorenzoni, Paolo et al.

In: International mathematics research notices, Vol. 2022, No. 21, 11.2022, p. 16730–16778.

Research output: Contribution to journal › Article › peer-review

Harvard

Arsie, A, Buryak, A, Lorenzoni, P & Rossi, P 2022, 'Riemannian F-Manifolds, Bi-Flat F-Manifolds, and Flat Pencils of Metrics', International mathematics research notices, vol. 2022, no. 21, pp. 16730–16778. https://doi.org/10.1093/imrn/rnab203

APA

Arsie, A., Buryak, A., Lorenzoni, P., & Rossi, P. (2022). Riemannian F-Manifolds, Bi-Flat F-Manifolds, and Flat Pencils of Metrics. International mathematics research notices, 2022(21), 16730–16778. https://doi.org/10.1093/imrn/rnab203

Vancouver

Arsie A, Buryak A, Lorenzoni P, Rossi P. Riemannian F-Manifolds, Bi-Flat F-Manifolds, and Flat Pencils of Metrics. International mathematics research notices. 2022 Nov;2022(21):16730–16778. Epub 2021 Aug 5. doi: 10.1093/imrn/rnab203

Author

Arsie, Alessandro ; Buryak, Alexandr ; Lorenzoni, Paolo et al. / Riemannian F-Manifolds, Bi-Flat F-Manifolds, and Flat Pencils of Metrics. In: International mathematics research notices. 2022 ; Vol. 2022, No. 21. pp. 16730–16778.

BibTeX

@article{85df081d5f1549cfa1e193833be878d0,
title = "Riemannian F-Manifolds, Bi-Flat F-Manifolds, and Flat Pencils of Metrics",
abstract = "In this paper, we study relations between various natural structures on F-manifolds. In particular, given an arbitrary Riemannian F-manifold, we present a construction of a canonical flat F-manifold associated to it. We also describe a construction of a canonical homogeneous Riemannian F-manifold associated to an arbitrary exact homogeneous flat pencil of metrics satisfying a certain non-degeneracy assumption. In the last part of the paper, we construct Legendre transformations for Riemannian F-manifolds.",
keywords = "DARBOUX-EGOROV SYSTEM, COUPLED KDV EQUATIONS, DIFFERENTIAL GEOMETRY, INTEGRABLE SYSTEMS, PAINLEVE, INVARIANTS",
author = "Alessandro Arsie and Alexandr Buryak and Paolo Lorenzoni and Paolo Rossi",
note = "This work was supported by the Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1675 [to A.B.] with the Ministry of Science and Higher Education of the Russian Federation; and the European Commission H2020-MSCA-RISE-2017 [Project No. 778010 IPaDEGAN to P.L.].",
year = "2022",
month = nov,
doi = "10.1093/imrn/rnab203",
language = "English",
volume = "2022",
pages = "16730–16778",
journal = "International mathematics research notices",
issn = "1073-7928",
publisher = "OXFORD UNIV PRESS INC",
number = "21",

}

RIS

TY - JOUR

T1 - Riemannian F-Manifolds, Bi-Flat F-Manifolds, and Flat Pencils of Metrics

AU - Arsie, Alessandro

AU - Buryak, Alexandr

AU - Lorenzoni, Paolo

AU - Rossi, Paolo

N1 - This work was supported by the Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1675 [to A.B.] with the Ministry of Science and Higher Education of the Russian Federation; and the European Commission H2020-MSCA-RISE-2017 [Project No. 778010 IPaDEGAN to P.L.].

PY - 2022/11

Y1 - 2022/11

N2 - In this paper, we study relations between various natural structures on F-manifolds. In particular, given an arbitrary Riemannian F-manifold, we present a construction of a canonical flat F-manifold associated to it. We also describe a construction of a canonical homogeneous Riemannian F-manifold associated to an arbitrary exact homogeneous flat pencil of metrics satisfying a certain non-degeneracy assumption. In the last part of the paper, we construct Legendre transformations for Riemannian F-manifolds.

AB - In this paper, we study relations between various natural structures on F-manifolds. In particular, given an arbitrary Riemannian F-manifold, we present a construction of a canonical flat F-manifold associated to it. We also describe a construction of a canonical homogeneous Riemannian F-manifold associated to an arbitrary exact homogeneous flat pencil of metrics satisfying a certain non-degeneracy assumption. In the last part of the paper, we construct Legendre transformations for Riemannian F-manifolds.

KW - DARBOUX-EGOROV SYSTEM

KW - COUPLED KDV EQUATIONS

KW - DIFFERENTIAL GEOMETRY

KW - INTEGRABLE SYSTEMS

KW - PAINLEVE

KW - INVARIANTS

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85158041203&origin=inward&txGid=ca9bd283188ff03291a37eab60657054

UR - https://www.mendeley.com/catalogue/40948295-f687-351e-be9f-3e7baa8aad1c/

U2 - 10.1093/imrn/rnab203

DO - 10.1093/imrn/rnab203

M3 - Article

VL - 2022

SP - 16730

EP - 16778

JO - International mathematics research notices

JF - International mathematics research notices

SN - 1073-7928

IS - 21

ER -

ID: 35561410