Skip to main content
Article thumbnail
Location of Repository

Projective convexity in P³ implies Grassmann convexity

By B. Shapiro and M. Shapiro

Abstract

In this note we introduce the notion of Grassmann convexity analogous to the wellknown notion of convexity for curves in real projective spaces. We show that the curve in G2,4 osculating to a convex closed curve in P³ is Grassmann-convex. This proves that the tangent developable (i.e. the hypersurface formed by all tangents) of any convex curve in P³ has the ‘degree’ equal to 4. Here by ‘degree’ of a real projective hypersurface we mean the maximal total multiplicity of its intersection with a line

Year: 2011
OAI identifier: oai:CiteSeerX.psu:10.1.1.185.1942
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://www.math.su.se/%7Eshapi... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.