By applications of theory of locally conformally Khler manifold and Bochner formula,we prove that under some conditions,a locally conformal compact Khler manifold must be Vaisman manifold,for example ：with ∫M（▽Bω）（B）＊1=0 and non-negative Ricci curvature,with non-negative Ricci curvature and dim（H1（M））=1,and that one special method is given which is sufficient to prove non-Vaisman manifold.%利用Bochner公式和局部共形Khler流形理论知识,主要证明了满足某些条件的局部共形Khler流形一定为Vaisman流形.如：具有非负Ricci曲率且∫m（▽Bω）（B）＊1=0;具有非负Rrcci曲率且dim（H1（M））=1等.同时,文中也给出一个判断非Vaisman流形的充分条件。
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