A Curvature identity on a 4-dimensional Riemannian manifold

Mathematics – Differential Geometry

Scientific paper

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10 pages

Scientific paper

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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