Vol. 306, No. 1, 2020

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 315: 1  2
Vol. 314: 1  2
Vol. 313: 1  2
Vol. 312: 1  2
Vol. 311: 1  2
Vol. 310: 1  2
Vol. 309: 1  2
Vol. 308: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Some classifications of biharmonic hypersurfaces with constant scalar curvature

Shun Maeta and Ye-Lin Ou

Vol. 306 (2020), No. 1, 281–290

We give some classifications of biharmonic hypersurfaces with constant scalar curvature. These include biharmonic Einstein hypersurfaces in space forms, compact biharmonic hypersurfaces with constant scalar curvature in a sphere, and some complete biharmonic hypersurfaces of constant scalar curvature in space forms and in a nonpositively curved Einstein space. Our results provide additional cases (Theorem 2.3 and Proposition 2.8) that support the conjecture that a biharmonic submanifold in Sm+1 has constant mean curvature, and two more cases that support Chen’s conjecture on biharmonic hypersurfaces (Corollaries 2.2 and 2.7).

PDF Access Denied

We have not been able to recognize your IP address 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:

biharmonic hypersurfaces, Einstein manifolds, constant scalar curvature, constant mean curvature
Mathematical Subject Classification 2010
Primary: 58E20
Secondary: 53C12
Received: 4 November 2018
Revised: 8 September 2019
Accepted: 12 December 2019
Published: 14 June 2020
Shun Maeta
Department of Mathematics
Shimane University
Ye-Lin Ou
Department of Mathematics
Texas A & M University
Commerce, TX
United States