## Tohoku Mathematical Journal

### Higher dimensional minimal submanifolds generalizing the catenoid and helicoid

#### 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}\$.

#### Article information

Source
Tohoku Math. J. (2), Volume 65, Number 1 (2013), 43-55.

Dates
First available in Project Euclid: 8 April 2013

https://projecteuclid.org/euclid.tmj/1365452624

Digital Object Identifier
doi:10.2748/tmj/1365452624

Mathematical Reviews number (MathSciNet)
MR3049639

Zentralblatt MATH identifier
1272.53004

#### Citation

Choe, Jaigyoung; Hoppe, Jens. Higher dimensional minimal submanifolds generalizing the catenoid and helicoid. Tohoku Math. J. (2) 65 (2013), no. 1, 43--55. doi:10.2748/tmj/1365452624. https://projecteuclid.org/euclid.tmj/1365452624