For Riemannian manifolds with boundary, the well‐known Gauss–Bonnet–Chern theorem gives an integral formula for the Euler characteristic of the manifold. Here we extend a proof by Avez to show that there is a similar result for manifolds with boundary endowed with a pseudo–Riemannian metric of arbitrary signature. In the case when the metric is Lorentzian there are some applications to general relativity. The generalized Gauss–Bonnet–Chern theorem also provides a formula for the gravitational kink.
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© 1995 American Institute of Physics.
1995
American Institute of Physics
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