Hiroshima Mathematical Journal

Biharmonic hypersurfaces in Riemannian symmetric spaces I

Jun-ichi Inoguchi and Toru Sasahara

Full-text: Open access

Abstract

We classify biharmonic geodesic spheres in the Cayley projective plane. Our results completes the classification of all biharmonic homogeneous hypersurfaces in simply connected compact Riemannian symmetric spaces of rank 1. In addition we show that complex Grassmannian manifolds, and exceptional Lie groups $F_4$ and $G_2$ admit proper biharmonic real hypersurfaces.

Article information

Source
Hiroshima Math. J., Volume 46, Number 1 (2016), 97-121.

Dates
First available in Project Euclid: 1 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1459525933

Digital Object Identifier
doi:10.32917/hmj/1459525933

Mathematical Reviews number (MathSciNet)
MR3482341

Zentralblatt MATH identifier
1350.58005

Subjects
Primary: 58E20: Harmonic maps [See also 53C43], etc.
Secondary: 53C43: Differential geometric aspects of harmonic maps [See also 58E20] 53C35: Symmetric spaces [See also 32M15, 57T15]

Keywords
Biharmonic maps Riemannian symmetric spaces Cayley projective plane complex Grassmannian manifolds Exceptional Lie groups F4, G2 Riemannian symmetric space of type FI homogeneous hypersurfaces

Citation

Inoguchi, Jun-ichi; Sasahara, Toru. Biharmonic hypersurfaces in Riemannian symmetric spaces I. Hiroshima Math. J. 46 (2016), no. 1, 97--121. doi:10.32917/hmj/1459525933. https://projecteuclid.org/euclid.hmj/1459525933


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