1996/04/24 by Xianghong Gong, Gong, Xianghong
Mathematics · #32 #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.CV #msc:32
paper · pdf · doi:10.48550/arxiv.math/9604203
arxiv created 1996/04/24 · openalex publication_date 1996/04/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We shall prove that there are totally real and real analytic embeddings of Sk in \ccn which are not biholomorphically equivalent if k≥ 5 and n=k+2[(k-1)/(4)]. We also show that a smooth manifold M admits a totally real immersion in \ccn with a trivial complex normal bundle if and only if the complexified tangent bundle of M is trivial. The latter is proved by applying Gromov's weak homotopy equivalence principle for totally real immersions to Hirsch's transversal fields theory.