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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… Click to show full 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 flat Riemannian manifold with positive scalar curvature and positive constant $$\sigma _2$$σ2 curvature is isometric to a quotient of the round $$\mathbb {S}^4$$S4.
Keywords:
riemannian manifolds;
compact riemannian;
curvature;
weyl curvature;
curvature positive;
harmonic weyl
Journal Title: Results in Mathematics
Year Published: 2019
Link to full text (if available)
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Journal Title: Results in Mathematics
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!