Some Results on Generalized Sasakian Space Forms

[1]P. Alegre, D. E. Blair and A. Carriazo, Generalized Sasakian space forms, Israel J. Math., 141 (2004), 157–183.AlegreP.BlairD. E.CarriazoA.Generalized Sasakian space formsIsrael J. Math.141200415718310.1007/BF02772217Search in Google Scholar

[2]P. Alegre and A. Carriazo, Structures on generalized Sasakian space forms, Differential Geom. Appl. 26 (2008), 656–666.AlegreP.CarriazoA.Structures on generalized Sasakian space formsDifferential Geom. Appl.26200865666610.1016/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), 923–941.AlegreP.CarriazoA.Submanifolds of generalized Sasakian space formsTaiwanese J. Math.13200992394110.11650/twjm/1500405448Search in Google Scholar

[4]P. Alegre and A. Carriazo, Generalized Sasakian space forms and conformal change of metric, Results Math., 59 (2011), 485–493.AlegreP.CarriazoA.Generalized Sasakian space forms and conformal change of metricResults Math.59201148549310.1007/s00025-011-0115-zSearch in Google Scholar

[5]M. Atceken, On generalized Sasakian space forms satisfying certain condiions on the concircular curvature tensor, Bull. Math. Anal. Appl., 6 (1) (2014), 1–8.AtcekenM.On generalized Sasakian space forms satisfying certain condiions on the concircular curvature tensorBull. Math. Anal. Appl.61201418Search in Google Scholar

[6]D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics Springer-Verlag, Berlin (1976) 509.BlairD. E.Contact manifolds in Riemannian geometryLecture Notes in Mathematics Springer-VerlagBerlin197650910.1007/BFb0079307Search in Google Scholar

[7]D. E. Blair, Riemannian geometry of Contact and symplectic manifolds, Birkhäuser Boston, 2002.BlairD. E.Riemannian geometry of Contact and symplectic manifoldsBirkhäuser Boston200210.1007/978-1-4757-3604-5Search in Google Scholar

[8]M. C. Chaki, On pseudo symmetric manifolds, Ann. St. Univ. Al I Cuza Iasi, 33 (1987).ChakiM. C.On pseudo symmetric manifoldsAnn. St. Univ. Al I Cuza Iasi331987Search in Google Scholar

[9]U. C. De and N. Guha, On generalized recurrent manifold, J. Nat. Acad. Math. 9 (1991), 85–92.DeU. C.GuhaN.On generalized recurrent manifoldJ. Nat. Acad. Math.919918592Search in Google Scholar

[10]U. C. De, A. Yildiz and A. F. Yaliniz, On ϕ-recurrent Kenmotsu manifolds, Turk J. Math., 33 (2009), 17–25.DeU. C.YildizA.YalinizA. F.On ϕ-recurrent Kenmotsu manifoldsTurk J. Math.3320091725Search in Google Scholar

[11]U. C. De and P. Majhi, ϕ-Semisymmetric generalized Sasakian space forms, Arab J. Math. Sci., 21 (2015), 170–178.DeU. C.MajhiP.ϕ-Semisymmetric generalized Sasakian space formsArab J. Math. Sci.212015170178Search in Google Scholar

[12]U. C. De and A. Sarkar, Some results on generalized Sasakian-space-forms, Thai J. Math., 8 (1) (2010), 1–10.DeU. C.SarkarA.Some results on generalized Sasakian-space-formsThai J. Math.812010110Search in Google Scholar

[13]U. C. De, A. Shaikh and B. Sudipta, On ϕ-Recurrent Sasakian manifolds, Novi Sad J. Math., 33 (13) (2003), 43–48.DeU. C.ShaikhA.SudiptaB.On ϕ-Recurrent Sasakian manifoldsNovi Sad J. Math.331320034348Search in Google Scholar

[14]R. Deszcz, On pseudosymmetric spaces, Bull. Soc. Math. Belg. Ser. A, 44 (1992), 1–34.DeszczR.On pseudosymmetric spacesBull. Soc. Math. Belg. Ser. A441992134Search in Google Scholar

[15]S. K. Hui and A. Sarkar, On the W₂-curvature tensor of generalized Sasakian space forms, Math. Pannonica, 23 (2012), 1–12.HuiS. K.SarkarA.On the W₂-curvature tensor of generalized Sasakian space formsMath. Pannonica23201211210.5402/2012/876276Search in Google Scholar

[16]S. K. Hui, S. Uddin and D. Chakraborty, Generalized Sasakian space forms whose metric is η-Ricci almost soliton, Differ. Geom. Dyn. Syst., 19 (2017), 45–55.HuiS. K.UddinS.ChakrabortyD.Generalized Sasakian space forms whose metric is η-Ricci almost solitonDiffer. Geom. Dyn. Syst.1920174555Search in Google Scholar

[17]S. K. Hui, D. G. Prakasha and V. Chavan, On generalized ϕ-recurrent generalized Sasakian-space-forms, Thai J. Math., 15(2), (2017) 323–332.HuiS. K.PrakashaD. G.ChavanV.On generalized ϕ-recurrent generalized Sasakian-space-formsThai J. Math.1522017323332Search in Google Scholar

[18]U. K. Kim, Conformally flat generalised Sasakian space forms and locally symmetric generalized Sasakian space forms, Note di mathematica, 26 (2006), 55–67.KimU. K.Conformally flat generalised Sasakian space forms and locally symmetric generalized Sasakian space formsNote di mathematica2620065567Search in Google Scholar

[19]G. P. Pokhariyal, Study of a new curvature tensor in a Sasakian manifold, Tensor N.S., 36(2) (1982), 222–225.PokhariyalG. P.Study of a new curvature tensor in a Sasakian manifoldTensor N.S.3621982222225Search in Google Scholar

[20]D.G. Prakasha, On extended generalized ϕ-recurrent Sasakian manifolds, J. Egyptian Math. Soc., 21 (2013), 25–31.PrakashaD.G.On extended generalized ϕ-recurrent Sasakian manifoldsJ. Egyptian Math. Soc.212013253110.1016/j.joems.2012.11.002Search in Google Scholar

[21]A. Sarkar and M. Sen, On ϕ-recurrent generalized Sasakian space forms, Lobachevskii J. Math., 33(3) (2012), 244–248.SarkarA.SenM.On ϕ-recurrent generalized Sasakian space formsLobachevskii J. Math.333201224424810.1134/S1995080212030146Search in Google Scholar

[22]A. A. Shaikh, T. Basu and S. Eyasmin, On the existence of ϕ-recurrent (LCS)_n-manifolds, Extracta Math., 23 (2008), 71–83.ShaikhA. A.BasuT.EyasminS.On the existence of ϕ-recurrent (LCS)_n-manifoldsExtracta Math.232008718310.4134/CKMS.2008.23.1.095Search in Google Scholar

[23]S. Pahana, T. Duttaa and A. Bhattacharyya, Ricci Soliton and η-Ricci Soliton on generalized Sasakian space forms, Filomat, 31(13) (2017), 4051–4062.PahanaS.DuttaaT.BhattacharyyaA.Ricci Soliton and η-Ricci Soliton on generalized Sasakian space formsFilomat311320174051406210.2298/FIL1713051PSearch in Google Scholar

[24]Z. I. Szabo, Structure theorem on Riemannian space satisfying (R(X,Y) · R) = 0. I. the local version, J. Differential Geom., 17 (1982), 531–582.SzaboZ. I.Structure theorem on Riemannian space satisfying (R(X,Y) · R) = 0. I. the local versionJ. Differential Geom.17198253158210.4310/jdg/1214437486Search in Google Scholar

[25]Shanmukha B. and Venkatesha, Some results on generalized Sasakian space forms with quarter symmetric metric connection, Asian Journal of Mathematics and Computer Research, 25 (3) 2018, 183–191.ShanmukhaB.VenkateshaSome results on generalized Sasakian space forms with quarter symmetric metric connectionAsian Journal of Mathematics and Computer Research2532018183191Search in Google Scholar

[26]T. Takahashi, Sasakian ϕ-symmetric space, Tohoku Math. J., 29 (91) (1977), 91–113.TakahashiT.Sasakian ϕ-symmetric spaceTohoku Math. J.299119779111310.2748/tmj/1178240699Search in Google Scholar

[27]Venkatesha and C. S. Bagewadi, On concircular ϕ-recurrent LP-Sasakian manifolds, Differ. Geom. Dyn. Syst., 10 (2008), 312–319.VenkateshaBagewadiC. S.On concircular ϕ-recurrent LP-Sasakian manifoldsDiffer. Geom. Dyn. Syst.102008312319Search in Google Scholar

[28]Venkatesha and Shanmukha B., W₂-curvature tensor on generalized Sasakian space forms, Cubo. A Mathematical Journal. Univ. Frontera, Dep. Mat. Estad., 20 (1) 2018, 17–29.VenkateshaShanmukhaB.W₂-curvature tensor on generalized Sasakian space formsCubo. A Mathematical Journal. Univ. Frontera, Dep. Mat. Estad.2012018172910.4067/S0719-06462018000100017Search in Google Scholar

[29]Venkatesha and Sumangala B., on M-projective curvature tensor of Generalised Sasakian space form, Acta Math., Univ. Comenianae, 2 (2013), 209–217.VenkateshaSumangalaB.on M-projective curvature tensor of Generalised Sasakian space formActa Math., Univ. Comenianae22013209217Search in Google Scholar

[30]K. Yano, Concircular geometry I. concircular transformations, Proc. Imp. Acad. Tokyo., 16 (1940), 195–200.YanoK.Concircular geometry I. concircular transformationsProc. Imp. Acad. Tokyo.16194019520010.3792/pia/1195579139Search in Google Scholar

[31]K. Yano and S. Bochner, Curvature and Betti numbers, Annals of Mathematics Studies 32, Princeton University Press, 1953.YanoK.BochnerS.Curvature and Betti numbersAnnals of Mathematics Studies 32,Princeton University Press195310.1515/9781400882205Search in Google Scholar