2004/02/23 by Dan Coman, Coman, Dan, Norman Levenberg +3
Mathematics · #26E10 #32U05 #32U15 #53A07 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.CV #math.DG #msc:26E10 #msc:32U05 #msc:32U15 #msc:53A07
paper · pdf · doi:10.48550/arxiv.math/0402379
arxiv created 2004/02/23 · openalex publication_date 2004/02/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct examples of C^∞ smooth submanifolds in \Bbb Cn and \Bbb Rn of codimension 2 and 1, which intersect every complex, respectively real, analytic curve in a discrete set. The examples are realized either as compact tori or as properly imbedded Euclidean spaces, and are the graphs of quasianalytic functions. In the complex case, these submanifolds contain real n-dimensional tori or Euclidean spaces that are not pluripolar while the intersection with any complex analytic disk is polar.