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THE JACOBI-ORTHOGONALITY IN INDEFINITE SCALAR PRODUCT SPACES.

Authors :
Lukić, Katarina
Source :
Publications de l'Institut Mathématique. 2024, Vol. 115 Issue 129, p33-44. 12p.
Publication Year :
2024

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 ∂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 Jacobidiagonalizable algebraic curvature tensor is Jacobi-orthogonal if and only if it is Osserman. [ABSTRACT FROM AUTHOR]

Subjects

Subjects :
*INNER product spaces
*CURVATURE

Details

Language :
English
ISSN :
03501302
Volume :
115
Issue :
129
Database :
Academic Search Index
Journal :
Publications de l'Institut Mathématique
Publication Type :
Academic Journal
Accession number :
177790579
Full Text :
https://doi.org/10.2298/PIM2429033l