Complex Tangencies to Embeddings of Heisenberg Groups and Odd-Dimensional Spheres

2015/06/26 by Ali M. Elgindi, Elgindi, Ali M.
Computer Science · Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Topological and Geometric Data Analysis #math.CV

paper · pdf · doi:10.48550/arxiv.1506.07991

Formal version published at: International Journal of Mathematics Vol. 25, No. 3 (2014), Article No. 1450028

arxiv created 2015/06/26 · openalex publication_date 2015/06/26 · arxiv updated 2015/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The notion of a complex tangent arises for embeddings of real manifolds into complex spaces. It is of particular interest when studying embeddings of real n-dimensional manifolds into ℂⁿ. The generic topological structure of the set complex tangents to such embeddings Mⁿ \hookrightarrow ℂⁿ takes the form of a (stratified) (n-2)-dimensional submanifiold of Mⁿ. In this paper, we generalize our results from our previous work for the 3-dimensional sphere and the Heisenberg group to obtain results regarding the possible topological configurations of the sets of complex tangents to embeddings of odd-dimensional spheres S^2n-1 \hookrightarrow ℂ^2n-1 by first considering the situation for the higher dimensional analogues of the Heisenberg group.

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