A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

The purpose of this thesis is to provide an intrinsic proof of a Gauss-Bonnet-Chern formula for complete Riemannian manifolds with finitely many conical singularities and asymptotically conical ends. A geometric invariant is associated to the link of both the conical singularities and the asymptotically conical ends and is used to quantify the Gauss-Bonnet defect of such manifolds. This invariant is constructed by contracting powers of a tensor involving the curvature tensor of the link. Moreover this invariant can be written in terms of the total Lipschitz-Killing curvatures of the link. A detailed study of the Lipschitz-Killing curvatures of Riemannian manifolds is presented as well as a complete modern version of Chern's intrinsic proof of the Gauss-Bonnet-Chern Theorem for compact manifolds with boundary.


Advisor(s):
Troyanov, Marc
Year:
2019
Publisher:
Lausanne, EPFL
Keywords:
Laboratories:
GR-TR




 Record created 2019-01-17, last modified 2019-05-09

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