Projective Surfaces and Pre-Normalized Blaschke Immersions of Codimension Two

Authors : Atsushi FUJİOKA, Hitoshi FURUHATA, Takeshi SASAKİ

Pages : 100-110

Doi:10.36890/iejg.591899

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Publication Date : 2016-04-30

Article Type : Research Paper

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