<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The use of the <italic>barycentre map</italic> between two copies of ℝ<italic><sup>n </sup></italic>, the first one with a metric without conjugate points, the second one with the canonical flat metric, allows to prove in a simplified way the fact that Riemannian tori without conjugate points are flat, as conjectured by Hopf in 1948 and proved definitively by Burago and Ivanov in 1994.</p>
</abstract>

The use of the barycentre map between two copies of ℝn , the first one with a metric without conjugate points, the second one with the canonical flat metric, allows to prove in a simplified way the fact that Riemannian tori without conjugate points are flat, as conjectured by Hopf in 1948 and proved definitively by Burago and Ivanov in 1994.

A simplified Proof of the Hopf Conjecture

Luca Sabatini, Dipartimento di Scienze di Base ed Applicate per l’Ingegneria

Università degli Studi di Roma La Sapienza

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"A simplified Proof of the Hopf Conjecture"}

The use of the barycentre map between two copies of ℝn , the first one with a metric without conjugate points, the second one with the canonical flat metric,...

A simplified Proof of the Hopf Conjecture

Published Online: May 27, 2024

Page range: 265 - 270

Received: Oct 09, 2022

Accepted: Feb 06, 2023

DOI: https://doi.org/10.2478/auom-2024-0014

Keywords
Manifolds without conjugate points, barycentre map

© 2024 Luca Sabatini, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A simplified Proof of the Hopf Conjecture

Published Online: May 27, 2024

Page range: 265 - 270

Received: Oct 09, 2022

Accepted: Feb 06, 2023

DOI: https://doi.org/10.2478/auom-2024-0014

KeywordsManifolds without conjugate points, barycentre map

© 2024 Luca Sabatini, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Manifolds without conjugate points, barycentre map