W-semisymmetric generalized Sasakian-space-forms

References

[1] 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

[2] P. Alegre and A. Carriazo, Structures on generalized Sasakian-space-forms, Differential Geom. Appl. 26 (2008), no. 6, 656–666. 10.1016/j.difgeo.2008.04.014Search in Google Scholar

[3] P. Alegre and A. Carriazo, Submanifolds of generalized Sasakian space forms, Taiwanese J. Math. 13 (2009), no. 3, 923–941. 10.11650/twjm/1500405448Search in Google Scholar

[4] P. Alegre and A. Carriazo, Generalized Sasakian space forms and conformal changes of the metric, Results Math. 59 (2011), no. 3–4, 485–493. 10.1007/s00025-011-0115-zSearch in Google Scholar

[5] D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. 509, Springer, Berlin, 1976. 10.1007/BFb0079307Search in Google Scholar

[6] D. E. Blair, Two remarks on contact metric structures, Tohoku Math. J. (2) 29 (1977), no. 3, 319–324. 10.2748/tmj/1178240602Search in Google Scholar

[7] S. Brendle and R. Schoen, Curvature, sphere theorems, and the Ricci flow, Bull. Amer. Math. Soc. (N.S.) 48 (2011), no. 1, 1–32. 10.1090/S0273-0979-2010-01312-4Search in Google Scholar

[8] S. K. Chaubey, Some properties of LP-Sasakian manifolds equipped with m-projective curvature tensor, Bull. Math. Anal. Appl. 3 (2011), no. 4, 50–58. Search in Google Scholar

[9] S. K. Chaubey, On weakly m-projectively symmetric manifolds, Novi Sad J. Math. 42 (2012), no. 1, 67–79. Search in Google Scholar

[10] S. K. Chaubey, Existence of N⁢(k)-quasi Einstein manifolds, Facta Univ. Ser. Math. Inform. 32 (2017), no. 3, 369–385. Search in Google Scholar

[11] S. K. Chaubey, Certain results on N⁢(k)-quasi Einstein manifolds, Afr. Mat. (2018), 10.1007/s13370-018-0631-z. 10.1007/s13370-018-0631-zSearch in Google Scholar

[12] S. K. Chaubey, On special weakly Ricci-symmetric and generalized Ricci-recurrent trans-Sasakian manifolds, Thai J. Math. 16 (2018), no. 3. Search in Google Scholar

[13] S. K. Chaubey and R. H. Ojha, On the m-projective curvature tensor of a Kenmotsu manifold, Differ. Geom. Dyn. Syst. 12 (2010), 52–60. Search in Google Scholar

[14] S. K. Chaubey, S. Prakash and R. Nivas, Some properties of m-projective curvature tensor in Kenmotsu manifolds, Bull. Math. Anal. Appl. 4 (2012), no. 3, 48–56. Search in Google Scholar

[15] U. C. De and A. Haseeb, On generalized Sasakian-space-forms with M-projective curvature tensor, Adv. Pure Appl. Math. 9 (2018), no. 1, 67–73. 10.1515/apam-2017-0041Search in Google Scholar

[16] U. C. De and P. Majhi, ϕ-semisymmetric generalized Sasakian space-forms, Arab J. Math. Sci. 21 (2015), no. 2, 170–178. Search in Google Scholar

[17] U. C. De and A. Sarkar, On the projective curvature tensor of generalized Sasakian-space-forms, Quaest. Math. 33 (2010), no. 2, 245–252. 10.2989/16073606.2010.491203Search in Google Scholar

[18] L. P. Eisenhart, Riemannian Geometry, Princeton University Press, Princeton, 1949. Search in Google Scholar

[19] R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), no. 2, 255–306. 10.4310/jdg/1214436922Search in Google Scholar

[20] R. S. Hamilton, The Ricci flow on surfaces, Mathematics and General Relativity (Santa Cruz 1986), Contemp. Math. 71, American Mathematical Society, Providence (1988), 237–262. 10.1090/conm/071/954419Search in Google Scholar

[21] R. Hit, On Sasakian manifold, Kyungpook Math. J. 13 (1973), 211–215. Search in Google Scholar

[22] S. K. Hui and D. Chakraborty, Generalized Sasakian-space-forms and Ricci almost solitons with a conformal Killing vector field, New Trends Math. Sci. 4 (2016), no. 3, 263–269. 10.20852/ntmsci.2016320381Search in Google Scholar

[23] U. K. Kim, Conformally flat generalized Sasakian-space-forms and locally symmetric generalized Sasakian-space-forms, Note Mat. 26 (2006), no. 1, 55–67. Search in Google Scholar

[24] R. Ojha, A note on the M-projective curvature tensor, Indian J. Pure Appl. Math. 8 (1977), no. 12, 1531–1534. Search in Google Scholar

[25] G. Perelman, The entropy formula for the Ricci flow and its geometric applications, preprint (2002), https://arxiv.org/abs/math/0211159. Search in Google Scholar

[26] G. Perelman, Ricci flow with surgery on three manifolds, preprint (2003), https://arxiv.org/abs/math/0303109. Search in Google Scholar

[27] G. P. Pokhariyal and R. S. Mishra, Curvature tensors and their relativistic significance. II, Yokohama Math. J. 19 (1971), no. 2, 97–103. Search in Google Scholar

[28] D. G. Prakasha, On generalized Sasakian-space-forms with Weyl-conformal curvature tensor, Lobachevskii J. Math. 33 (2012), no. 3, 223–228. 10.1134/S1995080212030110Search in Google Scholar

[29] A. Sarkar and U. C. De, Some curvature properties of generalized Sasakian-space-forms, Lobachevskii J. Math. 33 (2012), no. 1, 22–27. 10.1134/S1995080212010088Search in Google Scholar

[30] N. V. C. Shukla and R. J. Shah, Generalized Sasakian-sapce-forms with concircular curvature tensor, J. Rajasthan Acad. Phys. Sci. 10 (2011), no. 1, 11–24. Search in Google Scholar

[31] J. P. Singh, Generalized Sasakian space forms with m-projective curvature tensor, Acta Math. Univ. Comenian. (N.S.) 85 (2016), no. 1, 135–146. Search in Google Scholar

[32] Venkatesha and B. Sumangala, On M-projective curvature tensor of a generalized Sasakian space form, Acta Math. Univ. Comenian. (N.S.) 82 (2013), no. 2, 209–217. Search in Google Scholar