<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

Pubblicato online: 27 mag 2024

Pagine: 265 - 270

Ricevuto: 09 ott 2022

Accettato: 06 feb 2023

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

Parole chiave
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

Pubblicato online: 27 mag 2024

Pagine: 265 - 270

Ricevuto: 09 ott 2022

Accettato: 06 feb 2023

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

Parole chiaveManifolds 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.

Parole chiave
Manifolds without conjugate points, barycentre map