Projective convexity in P-3 implies Grassmann convexity

Citation
B. Shapiro et M. Shapiro, Projective convexity in P-3 implies Grassmann convexity, INT J MATH, 11(4), 2000, pp. 579-588
Citations number
13
Categorie Soggetti
Mathematics
Journal title
INTERNATIONAL JOURNAL OF MATHEMATICS
ISSN journal
0129167X → ACNP
Volume
11
Issue
4
Year of publication
2000
Pages
579 - 588
Database
ISI
SICI code
0129-167X(200006)11:4<579:PCIPIG>2.0.ZU;2-K
Abstract
In this note we introduce the notion of Grassmann convexity analogous to th e well-known notion of convexity for curves in real projective spaces. We s how that the curve in G(2,4) osculating to a convex closed curve in P-3 is Grassmann-convex. This proves that the tangent developable (i.e. the hypers urface formed by all tangents) of any convex curve in P-3 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.