Vol. 297, No. 1, 2018

 Recent Issues Vol. 299: 1  2 Vol. 298: 1  2 Vol. 297: 1  2 Vol. 296: 1  2 Vol. 295: 1  2 Vol. 294: 1  2 Vol. 293: 1  2 Vol. 292: 1  2 Online Archive Volume: Issue:
 The Journal Subscriptions Editorial Board Officers Special Issues Submission Guidelines Submission Form Contacts Author Index To Appear ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Other MSP Journals
Remarks on critical metrics of the scalar curvature and volume functionals on compact manifolds with boundary

Halyson Baltazar and Ernani Ribeiro, Jr.

Vol. 297 (2018), No. 1, 29–45
Abstract

We provide a general Bochner type formula which enables us to prove some rigidity results for $V$-static spaces. In particular, we show that an $n$-dimensional positive static triple with connected boundary and positive scalar curvature must be isometric to the standard hemisphere, provided that the metric has zero radial Weyl curvature and satisfies a suitable pinching condition. Moreover, we classify $V$-static spaces with nonnegative sectional curvature.

Keywords
Riemannian functional, critical metrics, static space, scalar curvature
Mathematical Subject Classification 2010
Primary: 53C21, 53C25
Secondary: 53C24