Projective Surfaces and Pre-Normalized Blaschke Immersions of Codimension Two

Year 2016, Volume: 9 Issue: 1, 100 - 110, 30.04.2016

Atsushi Fujioka Hitoshi Furuhata Takeshi Sasaki

https://doi.org/10.36890/iejg.591899

Abstract

   We prove that any non-degenerate surface in the projective 3-space has a local lift as a minimal

pre-normalized Blaschke immersion into the equicentroaffine 4-space. Furthermore, an indefinite

surface in the projective 3-space has a local lift as a pre-normalized Blaschke immersion into the

equicentroaffine 4-space satisfying the Einstein condition if and only if the surface is projectively

applicable to an affine sphere.

Keywords

projective surface, affine sphere, pre-normalized Blaschke immersion, centroaffine minimality, Einstein condition

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