CAJ | 학술논문

设x：M→An＋1是由定义在凸域Ω炒An上的某局部严格凸函数xn＋1＝f（x1，．．．，xn）给出的超曲面．考虑Hessian度量g ＝∑??2fxi?xjdxidxj ．若（M，g）是具有非负李奇曲率的紧致Hessian流形且仿射K?hler－Scalar曲率为零，作者证明了如果Δρ≤nρ2，则函数f一定是二次多项式，其中ρ＝[det（fij）]－1n＋2．
설x：M→An＋1시유정의재철역Ω초An상적모국부엄격철함수xn＋1＝f（x1，．．．，xn）급출적초곡면．고필Hessian도량g ＝∑??2fxi?xjdxidxj ．약（M，g）시구유비부리기곡솔적긴치Hessian류형차방사K?hler－Scalar곡솔위령，작자증명료여과Δρ≤nρ2，칙함수f일정시이차다항식，기중ρ＝[det（fij）]－1n＋2．
Let x:M→An+1 be a locally convex hypersurface, given by the graph of a convex function xn+1 =f(x1,...,xn) defined in a convex domain ΩAn .The Hessian metric g on M is considered, defined by g =∑??2 fxi?xj dxi dxj .Suppose ( M,g) is a compact Hessian manifold with nonnegative Ricci curvature , and with zero affine K?hler-Scalar curvature .It is proved that ifΔρ≤nρ2 , then f must be a quadratic polynomial , whereρ =[det(fij)] -1n+2 .