半不定内积与广义Minkowski空间
Semi-indefinite-inner-product and generalized Minkowski spaces
摘要：
本文建立了赋范线性空间和具有不定度量的线性空间的理论，文献中也称有限维Minkowski空间。本文的第一部分总结了半内积和不定内积的共同性质，定义了半不定内积和相应的结构，半不定度规空间。利用新积的概念，给出了嵌入半不定度规空间中的Minkowski空间的广义概念，其中包含了经典情况作为特殊情况。本文第二部分研究了实有限维广义Minkowski空间及其半径为$i$的球面。我们证明了它可以被看作是一个所谓的Minkowski-Finsler空间，如果它是关于线性等距的齐次空间，那么它的点的Minkowski-Finsler距离可以由Minkowski积确定。
英文摘要：
In this paper we parallelly build up the theories of normed linear spaces and of linear spaces with indefinite metric, called also Minkowski spaces for finite dimensions in the literature. In the first part of this paper we collect the common properties of the semi- and indefinite-inner-products and define the semi-indefinite-inner-product and the corresponding structure, the semi-indefinite-inner-product space. We give a generalized concept of Minkowski space embedded in a semi-indefinite-inner-product space using the concept of a new product, that contains the classical cases as special ones. In the second part of this paper we investigate the real, finite dimensional generalized Minkowski space and its sphere of radius $i$. We prove that it can be regarded as a so-called Minkowski-Finsler space and if it is homogeneous one with respect to linear isometries, then the Minkowski-Finsler distance its points can be determined by the Minkowski-product.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
