Finslerian convolution metrics and their special classes

TL;DR

This paper introduces the concept of convolution metrics in Finslerian Geometry, explores their properties, and characterizes special classes like Riemannian, Minkowskian, and Randers, providing examples and foundational insights.

Contribution

It defines and studies Finslerian convolution metrics, a novel concept, and characterizes their special subclasses with illustrative examples.

Findings

Characterization of Riemannian, Minkowskian, and Randers convolution metrics

Basic properties of Finslerian convolution metrics established

Examples of Finslerian convolutions provided

Abstract

Here, it is introduced a concept of convolution metric in Finslerian Geometry. This convolution metric is a kind of function obtained by a given mathematical operation between two Finslerian metrics. Some basic properties of the Finslerian convolution metrics are studied. Then it is characterized Finslerian convolution metrics which are of type Riemannian, Minkowskian as well as Randers. Furthermore, some examples of the Finslerian convolutions are given.