The mandala of Legendrian dualities for pseudo-spheres in Lorentz-Minkowski space and "flat" spacelike surfaces

• Izumiya Shyuichi

• Saji Kentaro

Abstract

Using the Legnedrian duarities between surfaces in pseudo-spheres in Lorentz-{Minkow}{ski} 4-space, we study various kind of flat surfaces in pseudo-spheres. We consider a surface in the pseudo-sphere and its dual surface. Flatness of a surface is defined by the degeneracy of the dual surface similar to the case for the Gauss map of a flat surface in the Euclidean space. We study singularities of these flat surfaces and dualities of singularities.

Journal

• Hokkaido University Preprint Series in Mathematics

  Hokkaido University Preprint Series in Mathematics 947 1-35, 2009-09-30

  Department of Mathematics, Hokkaido University

Keywords

• Legendrian duality
• Horo-spherical geometry
• Horo-flat surfaces
• Singularities
• Lorentz-Minkowski space
• Pseudo-spheres

Details

• CRID: 1390572174748846592
• NII Article ID: 120006459641
• DOI: 10.14943/84094
• HANDLE: 2115/69754
• Text Lang: en
• Data Source:
  • JaLC
  • IRDB
  • CiNii Articles
• Abstract License Flag: Allowed