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On the Gauss–Bonnet Formula in Riemann–Finsler Geometry
Author(s) -
Lackey Brad
Publication year - 2002
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s002460930100892x
Subject(s) - mathematics , christoffel symbols , connection (principal bundle) , gauss–bonnet theorem , riemann hypothesis , torsion (gastropod) , finsler manifold , riemannian geometry , mathematical analysis , pure mathematics , curvature , geometry , scalar curvature , mathematical physics , einstein , medicine , surgery
Using 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.