Abstract
For each $k$-dimensional complete minimal submanifold $M$ of $\boldsymbol{S}^n$ we construct a $(k+1)$-dimensional complete minimal immersion of $M\times \boldsymbol{R}$ into $\boldsymbol{R}^{n+2}$ and $(k+1)$-dimensional minimal immersions of $M\times \boldsymbol{R}$ into $\boldsymbol{R}^{2n+3},\boldsymbol{H}^{2n+3}$ and $\boldsymbol{S}^{2n+3}$. Also from the Clifford torus $M=\boldsymbol{S}^{k}(1/\sqrt{2})\times\boldsymbol{S}^{k}(1/\sqrt{2})$ we construct a $(2k+2)$-dimensional complete minimal helicoid in \boldsymbol{R}^{2k+3}$.
Citation
Jaigyoung Choe. Jens Hoppe. "Higher dimensional minimal submanifolds generalizing the catenoid and helicoid." Tohoku Math. J. (2) 65 (1) 43 - 55, 2013. https://doi.org/10.2748/tmj/1365452624
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