Generalized Minkowski space with changing shape

Abstract

Abstract. In earlier papers we changed the concept of the inner product to a more general one, to the so-called Minkowski product. This product changes on the tangent space hence we could investigate a more general structure than a Riemannian manifold. Particularly interesting such a model is when the negative direct component has dimension one and the model shows a certain space-time character. We will discuss this case here. We give a deterministic and a non-deterministic (random) variant of such a model. As we showed, the deterministic model can be defined also with a "shape function". Mathematics subject classification (2000). 46C50, 46C20, 53B40.

Isometries of Minkowski geometries

“…Nevertheless, the phrase "Minkowski space" is applied for two different theories: the theory of normed linear spaces and the theory of linear spaces with indefinite metric. It is interesting (see [10], [11], [12]) that these essentially distinct theories have similar axiomatic foundations. The axiomatic build-up of the theory of linear spaces with indefinite metric comes from H. Minkowski [25] and the similar system of axioms of normed linear spaces was introduced by Lumer much later in [19].…”

A Physical Space-modeled Approach to Lagrangian Equations with Bundle Structure for Minkowski 4-space

“…To follow these research in physics as a first step, we prefer to solve Lagrangian energy equations on the Minkowski 4-space which is based on a jet bundle structure.Works on generalized Minkowski spaces in the references [2,3,12], the time-space manifolds and studies for time-dependent Lagrangians can be seen in the references [4,17].…”

Relativity Theory in Time-space Manifold

“…In its own right, in a generalized space-time there is a theory of special relativity which was not developed in the above mentioned theoretical papers. In [7] the concept of generalized space-time model was extracted to a model called generalized Minkowski space with changing shape (briefly time-space). We gave two types of models, a non-deterministic (random) variation and a deterministic one.…”

“…The calculations in a generalized space-time model basically depend on a rule on the differentiability of the second variable of the Minkowski product. As a basic tool of investigations we proved in [7] that…”