Areal Spaces Based on Geometrical Theory of Parameter-Invariant Multiple Integrals

Areal spaces of different types have been studied by several authors, including Cartan [1], Davies [2], Kawaguchi [3] and several others. The study of areal spaces through parameter invariant multiple integrals is of great significance as the geometrical theory of areal spaces based on multiple integrals by Rund [8, 9] generalises both Finsler as well as Cartan spaces. Following Rund's approach, various aspects of areal spaces have been studied by Rastogi [5, 6, 7].