Totally skew embeddings of manifolds

Mohammad Ghomi, Sergei Tabachnikov

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

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
Volume258
Issue number3
DOIs
StatePublished - Mar 1 2008

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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