Geodesic
On the existence of a curvature tensor for given Jacobi operators
Filomat, Tome 37 (2023) no. 25, p. 8465

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DOI

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.
DOI : 10.2298/FIL2325465A
Classification : 53B20, 53B30
Keywords: Curvature tensor, Jacobi operators, Duality principle, Proportionality principle 
Vladica Andrejić; Katarina Lukić. On the existence of a curvature tensor for given Jacobi operators. Filomat, Tome 37 (2023) no. 25, p. 8465 . doi: 10.2298/FIL2325465A
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     title = {On the existence of a curvature tensor for given {Jacobi} operators},
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     pages = {8465 },
     year = {2023},
     volume = {37},
     number = {25},
     doi = {10.2298/FIL2325465A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2325465A/}
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