Affine Planar Geodesic Immersions with Maximal Codimension  

作　　者：Pawel WITOWICZ 

机构地区：[1]Rzeszow Universitu of Technology

出　　处：《Acta Mathematica Sinica,English Series》2010年第2期345-352,共8页数学学报（英文版）

基　　金：Supported by the KBN grant 1 P03A03426

摘　　要：This work gives a classification theorem for affine immersions with planar geodesics in the case where the codimension is maximal. Vrancken classified parallel affine immersions in this case and obtained, among others, generalized Veronese submanifolds. In this work it is shown that the immersions with planar geodesics are the same as the parallel ones in the considered case. A geometric interpretation of parallel immersions is also given： The affine immersions with pointwise planar normal sections （with respect to the equiaffine transversal bundle） are parallel. This result is verified for surfaces in R4 and for immersions with the maximal codimension.This work gives a classification theorem for affine immersions with planar geodesics in the case where the codimension is maximal. Vrancken classified parallel affine immersions in this case and obtained, among others, generalized Veronese submanifolds. In this work it is shown that the immersions with planar geodesics are the same as the parallel ones in the considered case. A geometric interpretation of parallel immersions is also given： The affine immersions with pointwise planar normal sections （with respect to the equiaffine transversal bundle） are parallel. This result is verified for surfaces in R4 and for immersions with the maximal codimension.

关 键 词：affine immersion GEODESIC transversal bundle normal section 

分 类 号：O186.12[理学—数学]