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 ↪ ℂn takes the form of a (stratified) (n-2)-dimensional submanifold 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 S2n-1 ↪ ℂ2n-1 by first considering the situation for the higher-dimensional analogues of the Heisenberg group.
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