Biharmonic submanifolds in manifolds with bounded curvature

• Maeta, Shun

Abstract

We consider a complete biharmonic submanifold [Formula: see text] in a Riemannian manifold with sectional curvature bounded from above by a non-negative constant [Formula: see text]. Assume that the mean curvature is bounded from below by [Formula: see text]. If (i) [Formula: see text], for some [Formula: see text], or (ii) the Ricci curvature of [Formula: see text] is bounded from below, then the mean curvature is [Formula: see text]. Furthermore, if [Formula: see text] is compact, then we obtain the same result without the assumption (i) or (ii). These are affirmative partial answers to Balmuş–Montaldo–Oniciuc conjecture.

Journal

• International journal of mathematics

  International journal of mathematics 27 (11), 1650089-1-1650089-15, 2016-10

  World Scientific Publishing

Keywords

• Biharmonic submanifolds
• constant mean curvature submanifolds
• BMO conjecture

Details

• CRID: 1050845763416360704
• NII Article ID: 120006352344
• NII Book ID: AA10754794
• ISSN: 0129167X
• ISSN: 17936519
• DOI: 10.1142/s0129167x16500890
• Web Site: http://ir.lib.shimane-u.ac.jp/40624
• Web Site: https://www.worldscientific.com/doi/pdf/10.1142/S0129167X16500890
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN