Generalizations of the Choe-Hoppe Helicoid and Clifford Cones in Euclidean Space

Abstract

By sweeping out L independent Clifford cones in R2N+2 via the multi-screw motion, we construct minimal submanifolds in RL(2N+2)+1. Also, we sweep out the L-rays Clifford cone (introduced in Sect. 2.3) in RL(2N+2) to construct minimal submanifolds in RL(2N+2)+1. Our minimal submanifolds unify various interesting examples: Choe-Hoppe's helicoid of codimension one, the cone over Lawson's ruled minimal surfaces in S-3, Barbosa-Dajczer-Jorge's ruled submanifolds, and Harvey-Lawson's volume-minimizing twisted normal cone over the Clifford torus 1/root 2S(N) x 1/root 2S(N).