Lorentz ${C}_{12}$-manifolds
Adel Delloum and Gherici Beldjilali
Volume 67, no. 1
(2024),
pp. 327–337
Published online: June 7, 2024
https://doi.org/10.33044/revuma.4064
Download PDF
Abstract
The object of the present paper is to study $C_{12}$-structures on a manifold with
Lorentzian metric. We focus here on Lorentzian $C_{12}$-structures, emphasizing their
relationship and analogies with respect to the Riemannian case. Several interesting
results are obtained. Next, we study Ricci solitons in Lorentzian $C_{12}$-manifolds.
References
-
G. Beldjilali, Slant curves in 3-dimensional $C_{12}$-manifolds, Balkan J. Geom. Appl. 27 no. 2 (2022), 13–25. MR Zbl
-
G. Beldjilali, Three-dimensional ${C}_{12}$-manifolds, Rev. Un. Mat. Argentina 67 no. 1 (2024), 1–14. DOI
-
B. Benaoumeur and G. Beldjilali, Ricci solitons on 3-dimensional $C_{12}$-manifolds, Balkan J. Geom. Appl. 27 no. 2 (2022), 26–36. MR Zbl
-
H. Bouzir, G. Beldjilali, and B. Bayour, On three dimensional $C_{12}$-manifolds, Mediterr. J. Math. 18 no. 6 (2021), Paper No. 239. DOI MR Zbl
-
S. de Candia and M. Falcitelli, Curvature of $C_5\oplus C_{12}$-manifolds, Mediterr. J. Math. 16 no. 4 (2019), Paper No. 105. DOI MR Zbl
-
A. M. Cherif, K. Zegga, and G. Beldjilali, On the generalised Ricci solitons and Sasakian manifolds, Commun. Math. 30 no. 1 (2022), 119–123. DOI MR Zbl
-
D. Chinea and C. Gonzalez, A classification of almost contact metric manifolds, Ann. Mat. Pura Appl. (4) 156 (1990), 15–36. DOI MR Zbl
-
R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geometry 17 no. 2 (1982), 255–306. DOI MR Zbl
-
P. Nurowski and M. Randall, Generalized Ricci solitons, J. Geom. Anal. 26 no. 2 (2016), 1280–1345. DOI MR Zbl
-
M. Okumura, Some remarks on space with a certain contact structure, Tohoku Math. J. (2) 14 (1962), 135–145. DOI MR Zbl
-
B. O'Neill, Semi-Riemannian geometry, Pure and Applied Mathematics 103, Academic Press, New York, 1983. MR Zbl