Construction of slant immersions. II (Q1344486)

This paper continues the author's previous one [Part I, cf. Bull. Inst. Math., Acad. Sin. 22, No. 2, 153-166 (1994; Zbl 0809.53064)]. The following result is proved: For any natural numbers \(n\), \(m\) with \(2n \leq m\) and any angle \(\alpha \in (0, \pi/2)\) there exists an \(\alpha\)- slant immersion of the open \(2n\)-cube \(I^{2n}\) into \(\mathbb{C}^m\), homothetic and full (in the sense of slantedness). A similar statement is obtained for spherical totally real immersions. The proofs are constructive. The method consists of making the construction for \(I^2\) immersed in \(\mathbb{C}^2\), \(\mathbb{C}^3\) and then using Cartesian products, direct sums and tensor products of immersions to construct the higher- dimensional immersions.