## Tohoku Mathematical Journal 2013 March SECOND SERIES VOL. 65, NO. 1

 Tohoku Math. J. 65 (2013), 43-55

Title HIGHER DIMENSIONAL MINIMAL SUBMANIFOLDS GENERALIZING THE CATENOID AND HELICOID

Author Jaigyoung Choe and Jens Hoppe

(Received January 6, 2012, revised May 14, 2012)
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}\$.

2000 Mathematics Subject Classification. Primary 53A10; Secondary 49Q10.

Key words and phrases. Minimal submanifold, catenoid, helicoid.