Spectral theoretical aspects of anisotropic relativistic models

Balan V.

Department Mathematics-Informatics, Politehnica University of Bucharest, Romania;

E-mail: Balan vladimir.balan@upb.ro

The present work is a survey of results from the spectral theory of covariant symmetric tensors (n-way arrays), which mainly deal with the fundamental geometric objects from anisotropic geometric models recently proposed by Russian specialists in Special Relativity. These objects play a major role in anisotropic structures, being provided by norms and by their related energy scalar fields; in this framework, we study from spectral point of view the m-th root n-way forms, the fundamental metric and the Cartan tensor fields of these models. The determined spectral data prove to be useful in describing properties of the indicatrices of the anisotropic structures, in pointing out their asymptotic properties and in constructing best rank-I approximations of the main covariant tensors - which provides both simple and consistent estimates for the original anisotropic structures.

Keywords: Finsler structures, n-way arrays, symmetric covariant tensors, Z-spectra, H-spectra, best rank-I approximation, Cartan tensor, Berwald-Moor metric, m-th root structures, fundamental tensor field.

DOI: 10.18698/2309-7604-2015-1-67-80

Article file: Balan.pdf