00923nas a2200133 4500008004100000245006400041210005700105260003700162300001400199490000700213520045100220100001700671856010100688 2002 eng d00aOn the Gauss–Bonnet Formula in Riemann–Finsler Geometry0 aGauss–Bonnet Formula in Riemann–Finsler Geometry bCambridge Univ Pressc2002/04/01 a329–3400 v343 aUsing Chern's method of transgression, the Euler class of a compact orientable Riemann–Finsler space is represented by polynomials in the connection and curvature matrices of a torsion-free connection. When using the Chern connection (and hence the Christoffel–Levi–Civita connection in the Riemannian case), this result extends the Gauss–Bonnet formula of Bao and Chern to Finsler spaces whose indicatrices need not have constant volume.1 aLackey, Brad uhttps://quics.umd.edu/publications/gauss%E2%80%93bonnet-formula-riemann%E2%80%93finsler-geometry