Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1894750 | Journal of Geometry and Physics | 2015 | 6 Pages |
Abstract
We use analytic continuation to derive the Euler–Lagrange equations associated to the Pfaffian in indefinite signature (p,q)(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.
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
P. Gilkey, J.H. Park,