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On the Gauss-Bonnet formula in Riemann-Finsler geometry. (English) Zbl 1039.53083
The author represents the Euler class of a compact orientable Riemann-Finsler manifold by polynomials in the connection and curvature matrices of a torsion-free connection using the Chern method of transgression. His results extend the Gauss-Bonnet formula of D. Bao and S. S. Chern [Ann. Math. 143, 233–252 (1996; Zbl 0849.53046)] to Finsler spaces whose indicatrices need not have constant volume.

MSC:
53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
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