Classification problems of biharmonic submanifolds

2014 Fiscal Year Final Research Report

• Project/Area Number: 25887044
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Shimane University (2014); Shumei University (2013)
• Principal Investigator: MAETA Shun 島根大学, 総合理工学研究科(研究院), 講師 (00709644)
• Project Period (FY): 2013-08-30 – 2015-03-31
• Keywords: 2重調和部分多様体 / 2重調和写像 / 調和写像 / 極小部分多様体 / k重調和写像 / Chen予想 / 完備リーマン多様体

Outline of Final Research Achievements

We studied polyharmonic maps of order k from a complete Riemannian manifold into a non-positively curved manifold. We got the following results.

We showed that biharmonic maps are harmonic under an integral condition. We applied this method into polyharmonic maps of order k. As a joint work with Prof. Urakawa and Prof. Nakauchi, we showed that triharmonic isometric immersion which have finite the 4-energy and finite the L4-norm of the tension field are harmonic. These results give affirmative partial answers to the global version of generalized Chen’s conjecture.

Free Research Field

微分幾何学