Spectra of symmetric tensors and m-root Finsler models

Abstract

The present work studies spectral properties of multilinear forms attached to the Berwald-Moor, Chernov and Bogoslovsky locally Minkowski Finsler geometric structures of m-root type. We determine eigenvalues and the corresponding eigenvectors (of type Z, H and E) of these forms, in the framework of symmetric tensors and multivariate homogeneous polynomials. The geometric relevance of the spectral data is emphasized, and the existent relations between spectra, polyangles and Riesz-type associated 1-forms of the corresponding geometric models, are described. As well, the best rank-one approximation for the 4-dimensional Berwald-Moor and Chernov cases, is derived.