On Compact Riemannian Manifolds with Harmonic Weyl Curvature
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DOI: 10.1007/s00025-019-0994-y
Abstract: We give some rigidity theorems for an n-dimensional ($$n\ge 4$$n≥4) compact Riemannian manifold with harmonic Weyl curvature, positive scalar curvature and positive constant $$\sigma _2$$σ2 curvature. Moreover, we prove that a 4-dimensional compact locally conformally… read more here.
Keywords: riemannian manifolds; compact riemannian; curvature; weyl curvature ... See more keywords
Einstein Four-Manifolds With Self-Dual Weyl Curvature of Nonnegative Determinant
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DOI: 10.1093/imrn/rnz238
Abstract: We prove that simply connected Einstein four-manifolds of positive scalar curvature are conformally Kähler if and only if the determinant of the self-dual Weyl curvature is positive. read more here.
Keywords: weyl curvature; einstein four; four manifolds; self dual ... See more keywords