On the volume functional of compact manifolds with harmonic Weyl tensor

Halyson Baltazar, Rondinelle Batista and Kelton Bezerra

Mathematische Nachrichten, 2023, vol. 296, issue 4, 1366-1379

Abstract: The main aim of this article is to give the complete classification of critical metrics of the volume functional on a compact manifold M with boundary ∂M$\partial M$ and under the harmonic Weyl tensor condition. In particular, we prove that a critical metric with a harmonic Weyl tensor on a simply connected compact manifold with the boundary isometric to a standard sphere Sn−1$\mathbb {S}^{n-1}$ must be isometric to a geodesic ball in a simply connected space form Rn$\mathbb {R}^n$, Hn$\mathbb {H}^n$, and Sn$\mathbb {S}^n$. To this end, we first conclude the classification of such critical metrics under the Bach‐flat assumption and then we prove that both geometric conditions are equivalent in this situation.

Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.202000389

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:296:y:2023:i:4:p:1366-1379

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().