Analytic Continuation, the Chern-gauss-bonnet Theorem, and the Euler-lagrange Equations in Lovelock Theory for Indefinite Signature Metrics
نویسندگان
چکیده
We use analytic continuation to derive the Euler-Lagrange equations associated to the Pfaffian in indefinite signature (p, q) directly from the corresponding result in the Riemannian setting. We also use analytic continuation to derive the Chern-Gauss-Bonnet theorem for pseudo-Riemannian manifolds with boundary directly from the corresponding result in the Riemannian setting. Complex metrics on the tangent bundle play a crucial role in our analysis and we obtain a version of the Chern-Gauss-Bonnet theorem in this setting for certain complex metrics. Subject Classification: 53C20
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