Three-dimensional $C_{12}$-manifolds

Authors

  • Gherici Beldjilali Laboratory of Quantum Physics and Mathematical Modeling (LPQ3M), University of Mascara, Algeria

DOI:

https://doi.org/10.33044/revuma.3088

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.

Downloads

Download data is not yet available.

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 $Qφ = φ Q$, 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 $C_5⊕ C_{12}$-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

Downloads

Published

2024-02-14

Issue

Section

Article