Totally skew embeddings of manifolds

Mohammad Ghomi, Serge Tabachnikov

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


We study a version of Whitney's embedding problem in projective geometry: What is the smallest dimension of an affine space that can contain an n-dimensional submanifold without any pairs of parallel or intersecting tangent lines at distinct points? This problem is related to the generalized vector field problem, existence of non-singular bilinear maps, and the immersion problem for real projective spaces. We use these connections and other methods to obtain several specific and general bounds for the desired dimension.

Original languageEnglish (US)
Pages (from-to)499-512
Number of pages14
JournalMathematische Zeitschrift
Issue number3
StatePublished - Mar 2008

All Science Journal Classification (ASJC) codes

  • General Mathematics


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