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arXiv · 2308.16655

The Jacobi-orthogonality in indefinite scalar product spaces

Katarina Lukić
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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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Katarina Lukić. 2023-08-31. The Jacobi-orthogonality in indefinite scalar product spaces. https://arxiv.org/abs/2308.16655

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