Biharmonic Homogeneous Submanifolds in Compact Symmetric Spaces

Hajime Urakawa,Takashi Sakai,Shinji Ohno

doi:10.1007/978-981-10-5556-0_27

Biharmonic Homogeneous Submanifolds in Compact Symmetric Spaces

Hajime Urakawa, Takashi Sakai + Show 1 more

https://doi.org/10.1007/978-981-10-5556-0_27

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Publication Date: Jan 1, 2017

Affiliation: Tohoku University, Tokyo Metropolitan University, Osaka City University

#Submanifolds In Compact Symmetric Spaces #Compact Symmetric Spaces + Show 8 more

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Abstract

This paper is a survey of our recent works on biharmonic homogeneous submanifolds in compact symmetric spaces (Biharmonic homogeneous submanifolds in compact symmetric spaces and compact Lie groups (in preparation), Biharmonic homogeneous hypersurfaces in compact symmetric spaces. Differ Geom Appl 43, 155–179 (2015)) [12, 13]. We give a necessary and sufficient condition for an isometric immersion whose tension field is parallel to be biharmonic. By this criterion, we study biharmonic orbits of commutative Hermann actions in compact symmetric spaces, and give some classifications.

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