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THE JACOBI-ORTHOGONALITY IN INDEFINITE SCALAR PRODUCT SPACES.
- 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 :
- *INNER product spaces
*CURVATURE
Subjects
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