Some results on Kenmotsu space forms
-
Shanmukha B
,
Suhad Ali Osman Abdallah
Abstract
The object of the present paper is to study Kenmotsu space forms satisfying pseudosymmetric, Ricci-pseudosymmetric and locally-ϕ-symmetric. Further we study the quasi-conformal flat and quasi-conformal semisymmetric Kenmotsu space forms.
Acknowledgements
The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through Large Groups Project under grant number (project number RGP.2/482/45.Academic Year 1444H).
References
[1] R. Abdi and E. Abedi, CR-hypersurfaces of a conformal Kenmotsu manifold satisfying certain shape operator conditions, Period. Math. Hungar. 73 (2016), no. 1, 83–92. 10.1007/s10998-016-0131-6Search in Google Scholar
[2]
O. Abu Arqub, H. Alsulami and M. Alhodaly,
Numerical Hilbert space solution of fractional Sobolev equation in
[3] O. Abu Arqub and N. Shawagfeh, Solving optimal control problems of Fredholm constraint optimality via the reproducing kernel Hilbert space method with error estimates and convergence analysis, Math. Methods Appl. Sci. 44 (2021), no. 10, 7915–7932. 10.1002/mma.5530Search in Google Scholar
[4] P. Alegre, D. E. Blair and A. Carriazo, Generalized Sasakian-space-forms, Israel J. Math. 141 (2004), 157–183. 10.1007/BF02772217Search in Google Scholar
[5] K. Amur and Y. B. Maralabhavi, On quasi-conformally flat spaces, Tensor (N. S.) 31 (1977), no. 2, 194–198. Search in Google Scholar
[6] K. Arslan, R. Ezentas, I. Mihai and C. Murathan, Contact CR-warped product submanifolds in Kenmotsu space forms, J. Korean Math. Soc. 42 (2005), no. 5, 1101–1110. 10.4134/JKMS.2005.42.5.1101Search in Google Scholar
[7] K. Arslan, R. Ezentas, I. Mihai, C. Murathan and C. Özgür, Ricci curvature of submanifolds in Kenmotsu space forms, Int. J. Math. Math. Sci. 29 (2002), no. 12, 719–726. 10.1155/S0161171202012863Search in Google Scholar
[8] M. Atc̣eken, Contact CR-warped product submanifolds in Kenmotsu space forms, Bull. Iranian Math. Soc. 39 (2013), no. 3, 415–429. Search in Google Scholar
[9] T. Q. Binh, L. Tamássy, U. C. De and M. Tarafdar, Some remarks on almost Kenmotsu manifolds, Math. Pannon. 13 (2002), no. 1, 31–39. Search in Google Scholar
[10] D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. 509, Springer, Berlin, 1976. 10.1007/BFb0079307Search in Google Scholar
[11] E. Cartan, Leçons sur la géométrie des espaces de Riemann, Gauthier-Villars, Paris, 1963. Search in Google Scholar
[12] U. C. De, J. B. Jun and A. K. Gazi, Sasakian manifolds with quasi-conformal curvature tensor, Bull. Korean Math. Soc. 45 (2008), no. 2, 313–319. 10.4134/BKMS.2008.45.2.313Search in Google Scholar
[13] U. C. De and G. Pathak, On 3-dimensional Kenmotsu manifolds, Indian J. Pure Appl. Math. 35 (2004), no. 2, 159–165. Search in Google Scholar
[14] R. Deszcz, On pseudosymmetric spaces, Bull. Soc. Math. Belg. Sér. A 44 (1992), no. 1, 1–34. Search in Google Scholar
[15] J.-B. Jun, U. C. De and G. Pathak, On Kenmotsu manifolds, J. Korean Math. Soc. 42 (2005), no. 3, 435–445. 10.4134/JKMS.2005.42.3.435Search in Google Scholar
[16] K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. (2) 24 (1972), 93–103. 10.2748/tmj/1178241594Search in Google Scholar
[17] M. Kon, Invariant submanifolds in Sasakian manifolds, Math. Ann. 219 (1976), no. 3, 277–290. 10.1007/BF01354288Search in Google Scholar
[18] C. Murathan, K. Arslan, R. Ezentas and I. Mihai, Warped product submanifolds in Kenmotsu space forms, Taiwanese J. Math. 10 (2006), no. 6, 1431–1441. 10.11650/twjm/1500404566Search in Google Scholar
[19] A. Olteanu, Contact CR-doubly warped product submanifolds in Kenmotsu space forms, JIPAM. J. Inequal. Pure Appl. Math. 10 (2009), no. 4, Article ID 119. Search in Google Scholar
[20] J. A. Oubiña, New classes of almost contact metric structures, Publ. Math. Debrecen 32 (1985), no. 3–4, 187–193. 10.5486/PMD.1985.32.3-4.07Search in Google Scholar
[21] G. Pitiş, A remark on Kenmotsu manifolds, Bul. Univ. Braşov Ser. C 30 (1988), 31–32. Search in Google Scholar
[22] B. Shanmukha and V. Venkatesha, Some Ricci solitons on Kenmotsu manifold, J. Anal. 28 (2020), no. 4, 1155–1164. 10.1007/s41478-020-00243-zSearch in Google Scholar
[23]
Z. I. Szabó,
Structure theorems on Riemannian spaces satisfying
[24] T. Takahashi, Sasakian ϕ-symmetric spaces, Tohoku Math. J. (2) 29 (1977), no. 1, 91–113. 10.2748/tmj/1178240699Search in Google Scholar
[25] S. Tanno, The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. J. (2) 21 (1969), 21–38. 10.2969/jmsj/02120270Search in Google Scholar
[26] L. Verstraelen, Comments on pseudo-symmetry in the sense of Ryszard Deszcz, Geometry and Topology of Submanifolds, World Scientific, River Edge (1994), 199–209. Search in Google Scholar
[27] S. Yadav and D. L. Suthar, On three-dimensional generalized Sasakian space forms, Afr. J. Math. Comput. Sci. Res. 5 (2012), 17–22. 10.5897/AJMCSR11.098Search in Google Scholar
[28] K. Yano and S. Sawaki, Riemannian manifolds admitting a conformal transformation group, J. Differential Geom. 2 (1968), 161–184. 10.4310/jdg/1214428253Search in Google Scholar
© 2025 Walter de Gruyter GmbH, Berlin/Boston
