Polyharmonic maps of order with finite
k-energy into Euclidean spaces
Author:
Shun Maeta
Journal:
Proc. Amer. Math. Soc. 143 (2015), 2227-2234
MSC (2010):
Primary 58E20; Secondary 53C43
DOI:
https://doi.org/10.1090/S0002-9939-2014-12382-3
Published electronically:
November 24, 2014
MathSciNet review:
3314128
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We consider polyharmonic maps of order
from a complete Riemannian manifold into the Euclidean space and let
be a real constant satisfying
.
If
and
then
is a polyharmonic map of order
.
If
and
, then
is a polyharmonic map of order
. Here,
and
. As a corollary, we give an affirmative partial answer to the generalized Chen conjecture.
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Additional Information
Shun Maeta
Affiliation:
Faculty of Tourism and Business Management, Shumei University, Chiba 276-0003, Japan
Address at time of publication:
Division of Mathematics, Shimane University, Nishikawatsu 1060 Mat-sue, 690-8504, Japan
Email:
shun.maeta@gmail.com, maeta@riko.shimane-u.ac.jp
DOI:
https://doi.org/10.1090/S0002-9939-2014-12382-3
Keywords:
Polyharmonic maps of order $k$,
biharmonic maps,
generalized Chen's conjecture,
Chen's conjecture
Received by editor(s):
October 3, 2013
Published electronically:
November 24, 2014
Additional Notes:
This work was supported by the Grant-in-Aid for Research Activity Start-up, No. 25887044, Japan Society for the Promotion of Science.
Communicated by:
Lei Ni
Article copyright:
© Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.