Holomorphic centroaffine immersions and the Lelieuvre correspondence

The rigidity and intrinsic characterization of holomorphic centroaffine immersions are given. We also obtain a method to construct nondegenerate holomorphic affine hypersurfaces from centroaffine immersions and metrics satisfying some conditions. Mathematics subject classification: 53A15.     

Syntheses of 2,6-Anhydro-3-Deoxy-D-Glycero-D-Galacto-Non-2-Enonic Acid (Kdn2En) and Its Hydrogenation Products 1

Abstract

Methyl 4,5,7,8,9-penta-O-acetyl-2,6-anhydro-3-deoxy-D-glycero-D-galacto-enonate (5) was synthesized from KDN methyl ester 2 with a catalytic amount of concentrated sulfuric acid in acetic anhydride, or from 2-chloro-KDN methyl ester 4 with DBU in good yield. Hydrogenation of 4 and 5 with 10% Pd-C gave 2-deoxy-2-H_ax-KDN 8 and 2-deoxy-2-H_eq-KDN derivative 11 in high yield, respectively. The structures of these compounds were elucidated from the MS, elemental analysis, ¹H NMR and ¹³C NMR data.