Kahler流形上有关Bakry-Emery曲率的Schur引理

摘要

This paper is to derive a Schur's lemma for Bakry-Emery Ricci curvature onK(a)hler manifolds.That is,the equation Ri(j) + fi(j) =λgi(j) with two smooth real-valued functions f,λ is studied on K(a)hler manifolds.Bv the Bianchi identitv,we obtain that λ must be a constant.%本文研究了K(a)hler流形上有关Bakry-Emery曲率的Schur引理.即在K(a)hler流形上考虑方程Ri(j)+fi(j)=λgi(j),其中f,λ是光滑实值函数.利用Bianchi恒等式,得到了λ是常数.