Diophantine vectors in analytic submanifolds of Euclidean spaces  

作　　者：Rong-mei CAO~(1+) Jian-gong YOU~2 1 College of Science,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China 2 Department of Mathematics,Nanjing University,Nanjing 210093,China 

出　　处：《Science China Mathematics》2007年第9期1334-1338,共5页中国科学：数学（英文版）

基　　金：This work was partially supported by the National Natural Science Foundation of China (Grant No.10531050);the National Basic Research Program of China (Grant No.2007CB814800)

摘　　要：Let $\mathcal{M}$ be an m-dimensional analytic manifold in ? n . In this paper, we prove that almost all vectors in $\mathcal{M}$ (in the sense of Lebesgue measure) are Diophantine if there exists one Diophantine vector in $\mathcal{M}$ .Let M be an m-dimensional analytic manifold in R^n.In this paper,we prove that almost all vectors in M (in the sense of Lebesgue measure) are Diophantine if there exists one Diophantine vector in M.

关 键 词：diophantine vector analytic submanifold 32C05 

分 类 号：O186[理学—数学]