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ON THE GAUSS–BONNET FORMULA IN RIEMANN–FINSLER GEOMETRY

Published online by Cambridge University Press:  22 May 2002

BRAD LACKEY
BRAD LACKEY
Affiliation:
Department of Mathematics, University of Hull, Hull HU6 7RX B.Lackey@maths.hull.ac.uk
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Abstract

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.

Type
PAPERS
Information
Bulletin of the London Mathematical Society , Volume 34 , Issue 3 , May 2002 , pp. 329 - 340
Copyright
© The London Mathematical Society 2002

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