Finslerian Geometries: A Meeting of Minds by M. Anastasiei, D. Hrimiuc (auth.), P. L. Antonelli (eds.)

By M. Anastasiei, D. Hrimiuc (auth.), P. L. Antonelli (eds.)

The overseas convention on Finsler and Lagrange Geometry and its functions: a gathering of Minds, happened August 13-20, 1998 on the collage of Alberta in Edmonton, Canada. the most target of this assembly was once to aid acquaint North American geometers with the huge glossy literature on Finsler geometry and Lagrange geometry of the japanese and ecu faculties, each one with its personal venerable heritage, at the one hand, and to speak fresh advances in stochastic idea and Hodge conception for Finsler manifolds through the more youthful North American college, at the different. The cause used to be to collect practitioners of those faculties of suggestion in a Canadian venue the place there will be abundant chance to replace info and feature cordial own interactions. the current set of refereed papers starts off ·with the Pedagogical Sec­ tion I, the place introductory and short survey articles are offered, one from the japanese tuition and from the ecu institution (Romania and Hungary). those were ready for non-experts with the purpose of explaining uncomplicated issues of view. The part III is the most physique of labor. it really is prepared in alphabetical order, through writer. part II supplies a short account of every of those contribu­ tions with a brief reference checklist on the finish. extra large references are given within the person articles.

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42. Some Remarks on the Conformal Equivalence 51 16] Aikou, T. (1999) Confonnal Flatness of Complex Finsler Structures, Publ. Math. Debrecen, 54. 17] Aikou, T. (1998) The Extension Class of Holomorphic Vector Bundles Associated with a Fibration, Preprint. 18] Hashiguchi, M. (1976) On Confonnal Transfonnations of Finsler Metrics, J. Math. , 16, 25-50. 19] Ichijyo, Y. , 41, 171-178. 110] Ichijyo, Y. (1991) Conformally Flat Finsler Structures, J. Math. , 25, 13-25. 111] Ichijyo, Y. (1994) Kaehlerian Finsler Manifolds, J.

Coo manifold M and map P : TM - t R, (x, y) ~ P(x, y). Here x = (Xi) are coordinates on M and (x, y) = (xi, yi) are coordinates on the tangent manifold T M projected on M by T. The indices i,j, k, ... will run from 1 to n = dim M and the Einstein convention on summation is implied. e. ignoring their dependence on y, will be called Finsler objects as in [7] or d-objects as in [8]. e. VuTM = Ker(DT)u, u E TM, where DT means the differential of T, is spanned by (8i ). The d-objects can be expressed using (8i ).

1, a convex Finsler structure F on E is flat if and only if (E, F) is modeled on a complex Minkowski space and its associated Hermitian metric hp is flat. 2 Conformally flat Finsler structures We consider a conformal change F -+ F = e

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