Hiroshima Mathematical Journal

Biharmonic homogeneous submanifolds in compact symmetric spaces and compact Lie groups

Shinji Ohno, Takashi Sakai, and Hajime Urakawa

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Abstract

We give a necessary and su‰cient condition for orbits of commutative Hermann actions and actions of the direct product of two symmetric subgroups on compact Lie groups to be biharmonic in terms of symmetric triad with multiplicities. By this criterion, we determine all the proper biharmonic orbits of these Lie group actions under some additional settings. As a consequence, we obtain many examples of proper biharmonic homogeneous submanifolds in compact symmetric spaces and compact Lie groups.

Article information

Source
Hiroshima Math. J., Volume 49, Number 1 (2019), 47-115.

Dates
Received: 4 August 2017
Revised: 27 May 2018
First available in Project Euclid: 6 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1554516038

Digital Object Identifier
doi:10.32917/hmj/1554516038

Mathematical Reviews number (MathSciNet)
MR3936648

Zentralblatt MATH identifier
07090064

Subjects
Primary: 58E20: Harmonic maps [See also 53C43], etc.
Secondary: 53C43: Differential geometric aspects of harmonic maps [See also 58E20]

Keywords
symmetric space symmetric triad Hermann action harmonic map biharmonic map

Citation

Ohno, Shinji; Sakai, Takashi; Urakawa, Hajime. Biharmonic homogeneous submanifolds in compact symmetric spaces and compact Lie groups. Hiroshima Math. J. 49 (2019), no. 1, 47--115. doi:10.32917/hmj/1554516038. https://projecteuclid.org/euclid.hmj/1554516038


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