The Jacobi-orthogonality in indefinite scalar product spaces

2023/08/31 by Katarina Lukić, Lukić, Katarina
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #Elasticity and Material Modeling #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2308.16655

openalex publication_date 2023/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize the property of Jacobi-orthogonality to indefinite scalar product spaces. We compare various principles and investigate relations between Osserman, Jacobi-dual, and Jacobi-orthogonal algebraic curvature tensors. We show that every quasi-Clifford tensor is Jacobi-orthogonal. We prove that a Jacobi-diagonalizable Jacobi-orthogonal tensor is Jacobi-dual whenever J_X has no null eigenvectors for all nonnull X. We show that any algebraic curvature tensor of dimension 3 is Jacobi-orthogonal if and only if it is of constant sectional curvature. We prove that every 4-dimensional Jacobi-diagonalizable algebraic curvature tensor is Jacobi-orthogonal if and only if it is Osserman.

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