Abstract
This work is motivated by the works of W.Y. Hsiang and H.B. Lawson [7], Pages $12$ and $13$. In this paper, we deal with the following double fibration:\[ \xymatrix@R-0.5cm @C-0.5cm{ & (G,g) \ar[ld]_{\pi_1} \ar[rd]^{\pi_2} & \\ (G/H,h_1) && (K\backslash G,h_2) } \]We will show that every $K$-invariant minimal or biharmonic hypersurface $M$ in $(G/H,h_1)$ induces an $H$-invariant minimal or biharmonic hypersurface $\widetilde{M}$ in $(K\backslash G,h_2)$ by means of $\widetilde{M}:=\pi_2(\pi_1{}^{-1}(M))$ (cf. Theorems 3.2 and 4.1). We give a one to one correspondence between the class of all the $K$-invariant minimal or biharmonic hypersurfaces in $G/H$ and the one of all the $H$-invariant minimal or biharmonic hypersurfaces in $K\backslash G$ (cf. Theorem 4.2).
Funding Statement
Supported by the Grant-in-Aid for the Scientific Research, (C) No.18K03352, Japan Society for the Promotion of Science.
Citation
Hajime URAKAWA. "Harmonic maps and biharmonic maps for double fibrations of compact Lie groups." Hokkaido Math. J. 52 (3) 401 - 425, October 2023. https://doi.org/10.14492/hokmj/2021-558
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