@article {lackey2002gauss, title = {On the Gauss{\textendash}Bonnet Formula in Riemann{\textendash}Finsler Geometry}, journal = {Bulletin of the London Mathematical Society}, volume = {34}, number = {03}, year = {2002}, month = {2002/04/01}, pages = {329{\textendash}340}, publisher = {Cambridge Univ Press}, abstract = {Using Chern{\textquoteright}s method of transgression, the Euler class of a compact orientable Riemann{\textendash}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{\textendash}Levi{\textendash}Civita connection in the Riemannian case), this result extends the Gauss{\textendash}Bonnet formula of Bao and Chern to Finsler spaces whose indicatrices need not have constant volume.}, author = {Brad Lackey} }