Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 20 (2025), 217 -- 233

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This work is licensed under a Creative Commons Attribution 4.0 International License.

GENERALIZED SASAKIAN-SPACE-FORMS WITH A CONTACT CONFORMAL CURVATURE TENSOR

Sudhakar Kumar Chaubey, Sunil Yadav and Mehmet Akif Akyol

Abstract. The present paper deals with the study of generalized Sasakian-space-forms. We show that the Ricci operator commutes with φ. The necessary and sufficient conditions for the Ricci and φ-contact conformally flat generalized Sasakian-space-forms are proved. We validate our results by providing a non-trivial example of a generalized Sasakian-space-form.

2020 Mathematics Subject Classification: 53D10, 53C25, 53D15
Keywords: Sasakian manifolds; generalized Sasakian-space-forms; contact conformal curvature tensor

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References

  1. P. Alegre, D. E. Blair and A. Carriazo, Generalized Sasakian-space-forms, Israel J. Math. 141 (2004), 157--183. MR2063031. Zbl 1064.53026.

  2. P. Alegre and A. Carriazo, Structures on generalized Sasakian-space-forms, Differential Geom. Appl. 26 (2008), 656--666. MR2474428. Zbl 1156.53027.

  3. P. Alegre and A. Carriazo, Generalized Sasakian-space-forms and conformal changes of metric, Results Math. 59 (2011), 485--493. MR2793469. Zbl 1219.53048.

  4. A. Carriazo, P. Alegre, C. Özgür and S. Sular, New examples of generalized Sasakian-space-forms, Rend. Semin. Mat. Univ. Politec. Torino 73 (2015), 63--76. MR3641390. Zbl 1454.53043.

  5. K. Bang and J. Y. Kye, Vanishing of contact conformal curvature tensor on 3-dimensional Sasakian manifolds, Kangweon-Kyungki Math. Jour. 10 (2002), no. 2, 157--166.

  6. D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics, Vol. 509, Springer-Verlag, Berlin, 1976. MR467588. Zbl 0319.53026.

  7. D. E. Blair, Two remarks on contact metric structures, Tohoku Math. Journ. 29 (1977), 319--324. MR464108. Zbl 0376.53021.

  8. S. K. Chaubey and A. Yildiz, On Ricci tensor in the generalized Sasakian-space-forms, International Journal of Maps in Mathematics 2 (2019), no. 1, 131--147.

  9. S. K. Chaubey and S. K. Yadav, W-semisymmetric generalized Sasakian-space-forms, Adv. Pure Appl. Math. 10 (2019), no. 4, 427--436. MR4015211. Zbl 1429.53064.

  10. S. K. Chaubey and Y. J. Suh, Ricci-Bourguignon solitons and Fischer-Marsden conjecture on generalized Sasakian-space-forms with β-Kenmotsu structure, J. Korean Math. Soc. 60 (2023), no. 2, 341--358. MR4553857. Zbl 1519.53038.

  11. U. C. De and P. Majhi, φ-semisymmetric generalized Sasakian-space-forms, Arab. J. Math. Sci. 21 (2015), 170--178. MR3376109. Zbl 1330.53037.

  12. M. K. Dwivedi, L. M. Fernández and M. M. Tripathi, The structure of some classes of contact metric manifolds, Georgian Math. J. 16 (2009), no. 2, 295--304. MR2562362. Zbl 1173.53316.

  13. S. K. Hui and D. G. Prakasha, On the C-Bochner curvature tensor of generalized Sasakian-space-forms, Proc. Nat. Acad. Sci. India Sect. A 85 (2015), no. 3, 401--405. MR3396570. Zbl 1325.53059.

  14. S. K. Hui, D. G. Prakasha and V. Chavan, On generalized φ-Recurrent generalized Sasakian-space-forms, Thai J. Math. 15 (2017), no. 2, 323--332. MR3696223. Zbl 1384.53046.

  15. J. C. Jeong, J. D. Lee, G. H. Oh and J. S. Pak, On the contact conformal curvature tensor, Bull. Korean Math. Soc. 27 (1990), no. 2, 133--142. MR1088539. Zbl 0726.53032.

  16. U. K. Kim, Conformally flat generalized Sasakian-space-forms and locally symmetric generalized Sasakian-space-forms, Note Mat. 26 (2006), 55--67. MR2267682. Zbl 1118.53025.

  17. J. S. Kim, J. Choi, C. Özgür and M. M. Tripathi, On the contact conformal curvature tensor of a contact metric manifold, Indian J. pure and appl. Math. 37 (2006), no 4, 199--207. MR2273319. Zbl 1125.53066.

  18. H. Kitahara, K. Matsuo and J. S. Pak, A conformal curvature tensor field on Hermitian manifolds, J. Korean Math. Soc. 27 (1990), no. 1, 7--17. MR1061071. Zbl 0711.53020.

  19. C. W. Lee, J. W. Lee, Gabriel-Eduard Vîlcu and D. W. Yoon, Optimal inequalities for the casorati curvatures of submanifolds of generalized space forms endowed with semi-symmetric metric connections, Bull. Korean Math. Soc. 52 (2015), No. 5, 1631--1647. MR3406025. Zbl 1330.53071.

  20. C. Özgür and S. Sular, On N(k)-contact metric manifolds satisfying certain conditions, SUT J. Math. 44 (2008), no. 1, 89--99. MR2450137. Zbl 1166.53020.

  21. J. S. Pak and Y. J. Shin, A note on contact conformal curvature tensor, Commun. Korean Math. Soc. 13 (1998), no. 2, 337--343. MR1716614. Zbl 0970.53028.

  22. J. S. Pak, Y. J. Shin and J. C. Jeong, Contact metric manifolds with vanishing contact conformal curvature tensor fields, Kyungpook Math. J. 35 (1996), 747--751. MR1678221. Zbl 1074.53505.

  23. S. K. Yadav and S. K. Chaubey, Certain results on submanifolds of generalized Sasakian space forms, Honam Mathematical J. 42 (2020), no. 1, 123--137. MR4116427. Zbl 1448.53021.



Sudhakar Kumar Chaubey - Corresponding author
Section of Mathematics, Department of Information Technology,
College of Computing and Information Sciences,
University of Technology and Applied Sciences, Shinas - 324, Oman.
e-mail: sk22_math@yahoo.co.in


Sunil Yadav
Department of Applied Science and Humanities,
United College of Engineering & Research, A-31 UPSIDC Industrial Areas,
U.P., India.
e-mail: prof_sky16@yahoo.com


Mehmet Akif Akyol
Uşak University,
Faculty of Engineering and Natural Sciences, Department of Mathematics,
64, Uşak, Türkiye.
e-mail: mehmet.akyol@usak.edu.tr



https://www.utgjiu.ro/math/sma