Abstract
Throughout this paper, let M be a compact orientable manifold without boundary. A Finsler structure is a most natural generalization of a Riemannian metric. Rather than endow each tangent space T x M with an inner product, the geometry is induced by a Minkowski norm F(x, y) on T x M. We will assume that the function F on TM is positive homogeneous of degree one in y, and smooth at y≠ 0. The fundamental tensor is defined as, where F yi means, etc. It is presumed to be positive definite. Since the g ij’s are homogeneous of degree zero in y, they are well-defined quantities on the sphere bundle S M, provided that we regard the y i’ s as homogeneous coordinates.
Research supported by the Izaak W. Killam Trust.
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© 1998 Springer Science+Business Media Dordrecht
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Bao, D., Lackey, B. (1998). A Geometric Inequality and a Weitzenböck Formula for Finsler Surfaces. In: Antonelli, P.L., Lackey, B.C. (eds) The Theory of Finslerian Laplacians and Applications. Mathematics and Its Applications, vol 459. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5282-2_15
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DOI: https://doi.org/10.1007/978-94-011-5282-2_15
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