QUANTUM PHENOMENON OF THE ENERGY DENSITY OF A HARMONIC MAP TO A SPHERE  

作　　者：周振荣 

出　　处：《Acta Mathematica Scientia》2003年第1期41-45,共5页数学物理学报（B辑英文版）

基　　金：Research supported by the NNSF of China (10071021)

摘　　要：This paper proves that if the energy density of a harmonic map to a unit sphere varies between two successive half eigenvalues, then it must be one of them. Applying this result to the Gaussian maps of some submanifolds, the quantum phenomena of the square length of the second fundamental forms of these submanifolds is obtained. Some related topics are discussed in this note.This paper proves that if the energy density of a harmonic map to a unit sphere varies between two successive half eigenvalues, then it must be one of them. Applying this result to the Gaussian maps of some submanifolds, the quantum phenomena of the square length of the second fundamental forms of these submanifolds is obtained. Some related topics are discussed in this note.

关 键 词：Energy density EIGENVALUE the second fundamental form 

分 类 号：O174.51[理学—数学]