Riemannian F-Manifolds, Bi-Flat F-Manifolds, and Flat Pencils of Metrics-Reference-Cited by-同舟云学术

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

Published:2021-08-05 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Arsie Alessandro¹,Buryak Alexandr²³⁴,Lorenzoni Paolo⁵⁶,Rossi Paolo⁷

Affiliation:

1. Department of Mathematics and Statistics, The University of Toledo, 2801W Bancroft St, Toledo, OH 43606, USA

2. Faculty of Mathematics, National Research University Higher School of Economics, 6 Usacheva str., Moscow, 119048, Russian Federation

3. Center for Advanced Studies, Skolkovo Institute of Science and Technology, 1 Nobel str., Moscow, 143026, Russian Federation

4. Novosibirsk State University, 1 Pirogova str., Novosibirsk, 630090, Russian Federation

5. Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via Roberto Cozzi 53, I-20125 Milano, Italy

6. INFN Sezione di Milano-Bicocca, 20126 Milano, Italy

7. Dipartimento di Matematica “Tullio Levi–Civita,” Università degli Studi di Padova, Via Trieste 63, 35121 Padova, Italy

Abstract

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.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnab203/39588549/rnab203.pdf

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2. Semisimple flat F-manifolds in higher genus;Arsie,2021

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