A Curvature identity on a 4-dimensional Riemannian manifold
classification
🧮 math.DG
keywords
identitycurvaturedimensionalriemanniancompactmanifoldapplicationsderived
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We give a curvature identity derived from the generalized Gauss-Bonnet formula for 4-dimensional compact oriented Riemannian manifolds. We prove that the curvature identity holds on any 4-dimensional Riemannian manifold which is not necessarily compact. We also provide some applications of the identity.
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