A Study on Curvature in Lorentzian Generalized Sasakian-Space-Forms and Its Applications
DOI:
https://doi.org/10.36676/jrps.v10.i1.1630Keywords:
Lorentzian, Sasakian-Space-Forms, Curvature, semisymmetric, Ricci, Differential GeometryAbstract
In this paper, we investigate the curvature properties of Lorentzian generalized Sasakian-space-forms. We establish the necessary and sufficient conditions for these manifolds to be projectively flat, conformally flat, conharmonically flat, and Ricci semisymmetric, exploring their interrelationships. Additionally, as an application of these theorems, we study the behavior of Ricci almost solitons on conformally flat Lorentzian generalized Sasakian-space-forms.
References
H. d. A. Gomes, “Classical gauge theory in Riem,” Journal of Mathematical Physics, vol. 52, no. 8, article 082501, 2011 DOI: https://doi.org/10.1063/1.3603990
T. T. Wu and C. N. Yang, “Concept of nonintegrable phase factors and global formulation of gauge fields,” Physical Review D, vol. 12, no. 12, pp. 3845–3857, 1975. DOI: https://doi.org/10.1103/PhysRevD.12.3845
D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Volume 203 of Progress in Mathematics, Birkhauser Boston, Inc., Boston, MA, USA, 2nd edition, 2010 DOI: https://doi.org/10.1007/978-0-8176-4959-3
P. Alegre, D. E. Blair, and A. Carriazo, “Generalized Sasakianspace-forms,” Israel Journal of Mathematics, vol. 141, no. 1, pp. 157–183, 2004. DOI: https://doi.org/10.1007/BF02772217
P. Alegre and A. Carriazo, “Semi-Riemannian generalized Sasakian space forms,” Bulletin of the Malaysian Mathematical Sciences Society, vol. 41, no. 1, pp. 1–14, 2014 DOI: https://doi.org/10.1007/s40840-015-0215-0
R. S. Hamilton, “Three-manifolds with positive Ricci curvature,” Journal of Differential Geometry, vol. 17, no. 2, pp. 255–306, 1982. DOI: https://doi.org/10.4310/jdg/1214436922
W. Batat, M. Brozos-Vázquez, E. García-Río, and S. GavinoFernández, “Ricci solitons on Lorentzian manifolds with large isometry groups,” Bulletin of the London Mathematical Society, vol. 43, no. 6, pp. 1219–1227, 2011. DOI: https://doi.org/10.1112/blms/bdr057
C. L. Bejan and M. Crasmareanu, “Second order parallel tensors and Ricci solitons in 3-dimensional normal paracontact geometry,” Annals of Global Analysis and Geometry, vol. 46, no. 2, pp. 117–127, 2014. DOI: https://doi.org/10.1007/s10455-014-9414-4
G. Calvaruso and A. Zaeim, “A complete classification of Ricci and Yamabe solitons of non-reductive homogeneous 4-spaces,” Journal of Geometry and Physics, vol. 80, pp. 15–25, 2014. DOI: https://doi.org/10.1016/j.geomphys.2014.02.007
S. Pigola, M. Rigoli, M. Rimoldi, and A. G. Setti, “Ricci almost solitons,” Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, vol. 10, no. 4, pp. 757–799, 2011. DOI: https://doi.org/10.2422/2036-2145.2011.4.01
K. L. Duggal, “Space time manifolds and contact structures,” International Journal of Mathematics and Mathematical Sciences, vol. 13, no. 3, pp. 545–553, 1990. DOI: https://doi.org/10.1155/S0161171290000783
G. Calvaruso and D. Perrone, “Contact pseudo-metric manifolds,” Differential Geometry and its Applications, vol. 28, no. 5, pp. 615–634, 2010 DOI: https://doi.org/10.1016/j.difgeo.2010.05.006
R. Kumar, R. Rani, and R. K. Nagaich, “On sectional curvatures of (ε)-Sasakian manifolds,” International Journal of Mathematics and Mathematical Sciences, vol. 2007, Article ID 93562, 8 pages, 2007. DOI: https://doi.org/10.1155/2007/93562
S. Bochner, “Curvature and Betti numbers,” The Annals of Mathematics, vol. 49, no. 2, pp. 379–390, 1948. DOI: https://doi.org/10.2307/1969287
B. O’Neill, Semi-Riemannian Geometry: With Applications to Relativity, Academic Press, 1983.
Y. Ishii, “On conharmonic transformations,” The Tensor Society Tensor New Series, vol. 7, pp. 73– 80, 1957. Physics, vol. 32, no. 7, pp. 1847–18i
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