Geometrical eigenproblem of various types higher order tensors in Riemannian space

Abstract

The geometrical eigenproblem (G-eigenproblem) is validated as an extension of the classical eigenproblem of a linear operator within Euclidean vector space. It is homogeneous and invariant, making it efficient and advantageous for tensors describing real phenomena, regardless of the representation, while determining their eigenspaces. The G-eigenproblem in Riemannian space will be defined not only for covariant tensors but also for mixed and contravariant ones. Achievements will be discussed and related to higher-order unit tensors.