Hermitian metrics with vanishing second Chern Ricci curvature

Published 19 Sep 2023 in math.DG and math.CV | (2309.10295v1)

Abstract: We describe a rigidity phenomenon exhibited by the second Chern Ricci curvature of a Hermitian metric on a compact complex manifold. This yields a characterisation of second Chern Ricci-flat Hermitian metrics on several types of manifolds as well as a range of non-existence results for such metrics.

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