Electronic Resource
Springer
Monatshefte für Mathematik
79 (1975), S. 233-252
ISSN:
1436-5081
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract By means of the general form of Stokes' theorem on manifolds a divergence theorem is derived for hypersurfaces which bound a compact region of ann-dimensional Finsler spaceF n . In general the integrand of then-fold volume integral will depend on the covariant derivatives of an arbitrary vector field which defines the element of support; certain conditions under which this dependence may be circumvented are discussed. The scalar curvature ofF n is expressed in terms of the divergence of a certain vector field: forn=2 this formula reduces to a particularly simple form, and its substitution into the aforementioned divergence theorem gives rise to a formula which represents a generalization of the classical Gauss-Bonnet Theorem.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01304076
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