LOCALLY CONFORMAL KÄHLER MANIFOLDS AND CONFORMAL SCALAR CURVATURE Kim, Jae-Man;
We show that on a compact locally conformal Khler manifold (dim ), is Khler if and only if its conformal scalar curvature k is not smaller than the scalar curvature s of everywhere. As a consequence, if a compact locally conformal Khler manifold is both conformally flat and scalar flat, then is Khler. In contrast with the compact case, we show that there exists a locally conformal Khler manifold with k equal to s, which is not Khler.
compact locally conformal Khler manifold;conformal scalar curvature;Khler;conformally flat and scalar flat;a locally conformal Khler manifold with k equal to s;
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