On the degeneration of harmonic sequences from surfaces into complex Grassmann manifolds

Wu Bing Ye

Address.
Department of Mathematics, Fuzhou, Fujian, 350108, P. R. China

E-mail. bingyewu@yahoo.com.cn

Abstract.
Let $f:M\to G(m,n)$ be a harmonic map from surface into complex Grassmann manifold. In this paper, some sufficient conditions for the harmonic sequence generated by $f$ to have degenerate $\partial ^{\prime }$-transform or $\partial ^{\prime \prime }$-transform are given.

AMSclassification. 53C42, 53B30.

Keywords. Complex Grassmann manifold, harmonic map, harmonic sequence, genus, the generalized Frenet formulae.