Differentiability of projective transformations in dimension 2

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2020-10-01 DOI:10.1515/advgeom-2019-0023

J. Lang

引用次数: 0

Abstract

Abstract It is proven by elementary methods that in dimension 2, every locally injective continuous map, sending the curves of a Ck-spray to curves of another Ck-spray as oriented point sets, is a Ck-diffeomorphism. This extends the result [1] for dimension three and higher from 1965.

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二维射影变换的可微性

摘要用初等方法证明了在维2中，每个局部内射连续映射，将一个Ck喷雾的曲线作为定向点集发送到另一个Ck喷雾的曲线，都是Ck微分同胚。这扩展了1965年以来三维及更高维度的结果[1]。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.