This article is available for purchase or by subscription. See below.
Abstract
|
We study closed four-dimensional manifolds. In particular, we show that under various
pinching curvature conditions (for example, the sectional curvature is no more than
of the
smallest Ricci eigenvalue), the manifold is definite. If restricting to a metric with
harmonic Weyl tensor, then it must be self-dual or anti-self-dual under the same
conditions. Similarly, if restricting to an Einstein metric, then it must be
either the complex projective space with its Fubini–Study metric, the round
sphere, or the quotient of one of these. Furthermore, we also classify Einstein
manifolds with positive intersection form and an upper bound on the sectional
curvature.
|
PDF Access Denied
We have not been able to recognize your IP address
18.97.14.91
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for
USD 40.00:
Keywords
rigidity, Hopf conjecture, definite, Bochner technique,
harmonic Weyl, Einstein
|
Mathematical Subject Classification
Primary: 53C25
|
Milestones
Received: 25 July 2020
Revised: 19 November 2020
Accepted: 22 January 2022
Published: 28 August 2022
|
|