Acta mathematica scientia,Series B ›› 2003, Vol. 23 ›› Issue (1): 41-45.

• Articles • Previous Articles     Next Articles

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)

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

CLC Number: 

  • 58E20
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