A simple proof of the Gauss-Bonnet-Chern formula for Finsler manifolds
classification
🧮 math.DG
keywords
formulagauss-bonnet-chernconnectionfinslermanifoldsproofsimplecartan
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From the point of view of index theory, we give a simple proof of a Gauss-Bonnet-Chern formula for all Finsler manifolds by the Cartan connection. Based on this, we establish a Gauss-Bonnet-Chern formula for any metric-compatible connection and also derive the Gauss-Bonnet-Chern formula of Lackey.
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