2022/09/14 by Vladica Andrejić, Andrejić, Vladica, Katarina Lukić +1
Engineering · Physics and Astronomy · #Elasticity and Material Modeling #Advanced Differential Geometry Research #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2209.06882
It is well known that the Jacobi operators completely determine the curvature tensor. The question of existence of a curvature tensor for given Jacobi operators naturally arises, which is considered and solved in the previous work. Unfortunately, although the published theorem is correct, its proof is incomplete because it contains some omissions, and the aim of this paper is to present a complete and accurate proof. We also generalize the main theorem to the case of indefinite scalar product space. Accordingly, we generalize the proportionality principle for Osserman algebraic curvature tensors.