摘要
设M^n是CP^n(4)中全实的2——调和等距浸入子流形,若M^n紧致,则J_M〔∑aijk(h_ijk^a)~2+(n+1)‖B(f)‖~2-(n+5)‖τ(f)‖~2-(2-1/n)‖B(f)‖~4-‖τ(f)‖·‖B(f)‖~3〕*1≤0,其中h_ij^a是等距浸入的第二基本形式的分量,h_ijk^a是h_ij^a共变导数,H_a=(h_ij^a),‖B(f)‖~2=∑a trH_a^2,‖τ(f)‖~2=∑a (trH_a)~2. 上述积分式蕴含了〔2〕中的一个结果。
Let M^n be a totally real 2--harmonic isometric immersed submanifolds of an n-dimmensional complex projective space cp^n(4) and let M^n be compact, thenwhere B(f) =B(f) =∑ aij h_(ij)~αω_i?ω_j?e_α is the second fundamental form of the immersion, h_α^(ijk)is the covariant differentiation of h_α^(ij), τ(f) = Σ αi h_(αii)e_α Moreover some characterizations of to-tally real2-harmonic isometric immersion are given.
