Locally conformal kähler manifolds and conformal scalar curvature

초록

We show that on a compact locally conformal Kähler manifold M2n (dim M2n=2n≥ 4), M2n is Kähler if and only if its conformal scalar curvature k is not smaller than the scalar curvature s of M2n everywhere. As a consequence, if a compact locally conformal Kähler manifold M2n is both conformally flat and scalar flat, then M2n is Kähler. In contrast with the compact case, we show that there exists a locally conformal Kähler manifold with k equal to s, which is not Kähler. © 2010 The Korean Mathematical Society.

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