Complex Spaces in Finsler, Lagrange and Hamilton Geometries
Complex Spaces in Finsler, Lagrange and Hamilton Geometries
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DOI：
10.1007/978-1-4020-2206-7
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发表时间：
2004-08
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影响因子：
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通讯作者：
G. Munteanu
中科院分区：
文献类型：
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作者：
G. Munteanu
从历史的角度来看，我们提交给本研究的理论起源于P. Finsler 1918年的著名论文（[Fi]）。在经典概念和传统分类中，芬斯勒几何还有一些推广，它们使用相同的工作技术，可以被认为是自几何：拉格朗日和汉密尔顿空间。芬斯勒几何有一个足够长的潜伏期，以至于很少有数学家（E. Cartan， L. Berwald, SS Chem， H. Rund）有耐心深入到张量的宇宙中，这使他们把它比作丛林。对于我们这些现在研究芬斯勒几何的人来说，很明显，在20世纪70年代，非线性连接概念的结晶（这个概念几乎和芬斯勒空间一样古老，[SZ4]）和工作技能进入了它的适应框架领域，实现了质的飞跃。松本先生（后来，在1986年，在一本专著[Ma3]中发表）得到的结果不仅引起了日本的兴趣，而且引起了罗马尼亚、匈牙利、加拿大和美国等其他国家的兴趣，这些国家建立了芬斯勒几何学派，目前得到了广泛的认可。
From a historical point of view, the theory we submit to the present study has its origins in the famous dissertation of P. Finsler from 1918 ([Fi]). In a the classical notion also conventional classification, Finsler geometry has besides a number of generalizations, which use the same work technique and which can be considered self-geometries: Lagrange and Hamilton spaces. Finsler geometry had a period of incubation long enough, so that few math ematicians (E. Cartan, L. Berwald, SS Chem, H. Rund) had the patience to penetrate into a universe of tensors, which made them compare it to a jungle. To aU of us, who study nowadays Finsler geometry, it is obvious that the qualitative leap was made in the 1970's by the crystallization of the nonlinear connection notion (a notion which is almost as old as Finsler space,[SZ4]) and by work-skills into its adapted frame fields. The results obtained by M. Matsumoto (coUected later, in 1986, in a monograph,[Ma3]) aroused interest not only in Japan, but also in other countries such as Romania, Hungary, Canada and the USA, where schools of Finsler geometry are founded and are presently widely recognized.