数学物理学报(英文版) ›› 2003, Vol. 23 ›› Issue (1): 41-45.

• 论文 • 上一篇    下一篇

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

 周振荣   

  1. Department of Mathematics, Central China Normal University, Wuhan 430079, China
  • 出版日期:2003-01-06 发布日期:2003-01-06
  • 基金资助:

    Research supported by the NNSF of China (10071021)

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

 ZHOU Zhen-Rong   

  1. Department of Mathematics, Central China Normal University, Wuhan 430079, China
  • Online:2003-01-06 Published:2003-01-06
  • Supported by:

    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 squarelength 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

Abstract:

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 squarelength of the second fundamental forms of these submanifolds is obtained. Some related topics are discussed in this note.

Key words: Energy density, eigenvalue, the second fundamental form

中图分类号: 

  • 58E20