Existence and non-existence of skew branes

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dc.creatorTabachnikov, S.
dc.creatorTyurina, Yu.
dc.date2005-04-23
dc.date.accessioned2026-07-07T05:19:23Z
dc.date.available2026-07-07T05:19:23Z
dc.descriptionFollowing recent work by Ghomi, Solomon and Tabachnikov, we study geometry and topology of skew branes. A skew brane is a codimension 2 submanifold in affine space such that the tangent spaces at any pair of distinct points are not parallel. We prove that if an oriented closed manifold has a non-zero Euler characteristic $ξ$ then it is not a skew brane; generically, the number of oppositely oriented pairs of parallel tangent spaces is not less than $(ξ^2)/4$. We also construct examples of skew odd-dimensional spheres and skew two-dimensional tori.
dc.identifierhttps://arxiv.org/abs/math/0504484
dc.identifierhttp://arxiv.org/abs/math/0504484
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74999
dc.subjectDifferential Geometry
dc.subjectAlgebraic Topology
dc.titleExistence and non-existence of skew branes
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