Three-dimensional $C_{12}$-manifolds
Gherici Beldjilali
Volume 67, no. 1
(2024),
pp. 1–14
Published online: February 14, 2024
https://doi.org/10.33044/revuma.3088
Download PDF
Abstract
The present paper is devoted to three-dimensional $C_{12}$-manifolds (defined by D. Chinea
and C. Gonzalez), which are never normal. We study their fundamental properties and give
concrete examples. As an application, we study such structures on three-dimensional Lie
groups.
References
-
D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics 203, Birkhäuser Boston, Boston, MA, 2002. DOI MR Zbl
-
D. E. Blair, T. Koufogiorgos, and R. Sharma, A classification of $3$-dimensional contact metric manifolds with $Q\varphi=\varphi Q$, Kodai Math. J. 13 no. 3 (1990), 391–401. DOI 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, 13 pp. DOI MR Zbl
-
C. P. Boyer, K. Galicki, and P. Matzeu, On eta-Einstein Sasakian geometry, Comm. Math. Phys. 262 no. 1 (2006), 177–208. 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, 23 pp. 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
-
Z. Olszak, Normal almost contact metric manifolds of dimension three, Ann. Polon. Math. 47 no. 1 (1986), 41–50. DOI MR Zbl
-
J. Patera, R. T. Sharp, P. Winternitz, and H. Zassenhaus, Invariants of real low dimension Lie algebras, J. Mathematical Phys. 17 no. 6 (1976), 986–994. DOI MR Zbl
-
K. Yano and M. Kon, Structures on manifolds, Series in Pure Mathematics 3, World Scientific, Singapore, 1984. MR Zbl