Hannaneh Faraji, Behzad Najafi, Tayebeh Tabtabaeifar

DOI Number
First page
Last page


We introduce the ∗-conformal curvature tensor and ∗η-Einstien manifolds in contact manifolds. We investigate this tensor in the three main classes of contact manifolds: Sasakian manifolds, Kenmotsu manifolds, and cosymplectic manifolds. We prove that a manifold is η-Einstienian if and only if be ∗η-Einstienian manifold.


∗-conformal curvature, ∗η-Einstien manifolds, Sasakian manifolds, Kenmotsu manifolds, Cosymplectic manifolds.

Full Text:



S. Amari and H. Nagaoka: Methods of information geometry. Amer. Math. Soc. 191 (2000).

D. E. Blair: Riemannian geometry of contact and symplectic manifolds. Springer Science and Business Media (2010).

D. E. Blair: The theory of quasi-Sasakian structures. J. Diff. Geom. 1 (1967), 331–381.

D. E. Blair: Two remarks on contact metric manifolds. Tohoku Math. J. 29 (1977), 319–324.

D. E. Blair, T. Koufogiorgos and R. Sharma: A classification of 3-dimensional contact metric manifolds with Qφ= φQ. Kodai. J. Math, 13 (3) (1990), 391–401.

M. C. Chaki and B. Gupta: On conformally symmetric spaces. Indian J. Math. 5, (1963) 113–122.

B. Y. Chen and K. Yano: Hypersurfaces of conformally flat spaces. Tensor (N. S) 26 (1972), 318–322.

B. Chen and K. Yano: Special conformally flat spaces and canal hypersurfaces. Tohoku. J. Math. 25 (2) (1973), 177–184.

U. C. De, J. B. Jun and A. K. Gazi: Sasakian manifolds with quasi-conformal curvature tensor. Bull. Korean Math. Soc. 45 (2) (2008), 313–319.

U. C. De, M. Majhi and Y. J. Suh: ∗-Ricci soliton on Sasakian 3-manifolds. Publ. Math. Debrecen 93 (2018), 241–252.

U. C. De, A. A. Shaikh and S. Biswas: On φ-recurrent Sasakian manifolds. Novi Sad J. Math. 33 (2) (2003), 43–48.

A. Derdzinski and W. Roter: On Conformally Symmetric Manifolds with Metrics of Indices 0 and 1. Tensor N. S. 31 (1977) 255–259.

M. S. El Naschie: G¨odel universe, dualities and high energy particles in E-infinity. Chaos, Solitons & Fractals, 25 (3) (2005), 759–764.

A. Ghosh and D. S. Patra: ∗-Ricci Soliton within the framework of Sasakian and (k, µ)-contact manifold. Int. J. Geom. methods modern Phys. 15 1850120 (2018).

S. I Goldberg and K. Yano: Integrebility of almost cosymplectic structures. Pacific J. Math. 31 (1969), 373–382.

T. Hamada: Real hypersurfaces of complex space forms in terms of Ricci ∗-tensor. Tokyo J. Math. 25 (2002) 473–483.

A. Haseeb, D. G. Prakasha and H. Harish: ∗-Conformal η-Ricci solotons on α-cosymplectic manifolds. International Journal of Analysis and Applications 12 (2) (2021), 165–179.

S. Ianus and D. Smaranda: Some remarkable structures on the product of an almost contact metric manifold with the real line. Soc. Sti. Mat., Univ. Timisoara, 1977.

K. Kenmotsu: A class of almost contact Riemannian manifolds. Tohoku Math. J. 24 (1972), 93–103.

H. N. Nickerson: On conformally symmetric spaces. Geometriae Dedicata 18 (1) (1985), 87–99.

D. S. Patra, A. Ali and F. Mofarreh: Geometry of almost contact metrics as almost ∗-Ricci solitons. arXiv e-prints (2021): arXiv-2101.

W. Slosarska: On some property of conformally symmetric manifold admitting a semi-symmetric metric connection. Demonstratio Math. 17 (4) (1984), 813–816.

S. Tachibana: On almost-analytic vectors in almost Kahlerian manifolds. Tohoku Math. J. 11 (1959), 247–265.

S. Tanno: Note on infinitesimal transformations over contact manifolds. Tohoku Mathematical Journal, Second Series, 14 (4) (1962), 416–430.

Y. Wang: Contact 3-manifolds and ∗-Ricci soliton. Kodai Math. J. 43 (2020), 256–267.

K. Yano: On semi-symmetric metric connections. Rev. Roumaine Math. Pures Appl. 15 (1970) 1579–1586.

K. Yano and S. Sawaki; Riemannian manifolds admitting a conformal transformation group. Journal of Differential Geometry 2 (2) (1968), 161–184.

G. Zhen, J. L. Cobrerizo, L. M. Ferandez and M. Fernadez: On ξ-conformally flat contact metric manifolds. Indian J. Pure. Appl. Math. 28 (1997), 725–734.

DOI: https://doi.org/10.22190/FUMI231216023F


  • There are currently no refbacks.

© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)