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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Acknowledgements
The second author was supported by Grant-in-Aid for Scientific Research (C) No. 26400073, Japan Society for the Promotion of Science. The third author was supported by Grant-in-Aid for Scientific Research (C) No. 25400154, Japan Society for the Promotion of Science.
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Ohno, S., Sakai, T., Urakawa, H. (2017). Biharmonic Homogeneous Submanifolds in Compact Symmetric Spaces. In: Suh, Y., Ohnita, Y., Zhou, J., Kim, B., Lee, H. (eds) Hermitian–Grassmannian Submanifolds. Springer Proceedings in Mathematics & Statistics, vol 203. Springer, Singapore. https://doi.org/10.1007/978-981-10-5556-0_27
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DOI: https://doi.org/10.1007/978-981-10-5556-0_27
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