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

摘要

This paper proves that if the energy density of a harmonic map to a unit spherevaries between two successive half eigenvalues, then it must be one of them. Applying thisresult to the Gaussian maps of some submanifolds, the quantum phenomena of the squarelength of the second fundamental forms of these submanifolds is obtained. Some relatedtopics are discussed in this note.