TY  - JOUR
T1  - On generic submanifold of Sasakian manifold with concurrent vector field
AU  - Yoldaş, Halil İbrahim
AU  - Eken Meriç, Şemsi
AU  - Yaşar, Erol
PY  - 2019
DA  - August
Y2  - 2019
DO  - 10.31801/cfsuasmas.445788
JF  - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
JO  - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.
PB  - Ankara University
WT  - DergiPark
SN  - 1303-5991
SP  - 1983
EP  - 1994
VL  - 68
IS  - 2
LA  - en
AB  - In the present paper, we deal with the generic submanifold admitting a Ricci soliton in Sasakian manifold endowed with concurrent vector field. Here, we find that there exists never any concurrent vector field on the invariant distribution D of generic submanifold M. Also, we provide a necessary and sufficient condition for which the invariant distribution D and anti-invariant distribution D^{⊥} of M are Einstein. Finally, we give a characterization for a generic submanifold of Sasakian manifold to be a gradient Ricci soliton.
KW  - Sasakian manifold
KW  - Ricci soliton
KW  - concurrent vector field
CR  - P. Alegre, Semi-Invariant Submanifolds of Lorentzian Sasakian Manifolds, \emph{Demonstratio Math.} 44:2(2011), 33-38.
CR  - M. Atçeken, S. Uddin, Semi-invariant submanifolds of a normal almost paracontact manifold, \emph{Filomat} 31(15) (2017), 4875-4887.
CR  - C. S. Bagewadi, G. Ingalahalli, Ricci solitons in Lorentzian $\alpha-$Sasakian manifolds, \emph{Acta Math. Acad. Paedagog. Nyh\'{a}zi. (N.S)} 28(1) (2012), 59-68.
CR  - C. L. Bejan, M. Crasmareanu, Second order parallel tensors and Ricci solitons in 3-simensional normal paracontact geometry, \emph{Ann. Glob. Anal. Geom.} 46(2014), 117-127.
CR  - A. Bejancu, N. Papaghiuc, Semi-invariant submanifolds of Sasakian manifold, \emph{An. St. Univ. AI. I. Cuza. Iasi} 27(1981), 163-170.
CR  - A. Bejancu, N. Papaghiuc, Semi-invariant submanifolds of a Sasakian space form, \emph{Colloq. Math.} 48(1984), 77-88.
CR  - A. Bejancu, Geometry of CR-submanifolds, Mathematics and Its Applications (East European Series), (1986).
CR  - D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 509(1976).
CR  - B.-Y. Chen, S. Deshmukh, Ricci solitons and concurrent vector fields, \emph{Balkan J. Geom. Appl.} 20(1) (2015), 14-25.
CR  - B.-Y. Chen, Classification of torqued vector fields and its applications to Ricci solitons, \emph{Kragujevac J. Math.} 41(2) (2017), 239-250.
CR  - K. L. Duggal, D. L. Jin, Generic lightlike submanifolds of an indefinite SasakianmManifold, \emph{Int. Electron. J. Geom.} 5(1) (2012), 108-119.
CR  - Ghosh, Certain contact metrics as Ricci almost solitons, \emph{Results Maths.} 65(2014), 81-94.
CR  - A. Ghosh, Kenmotsu 3-metric as a Ricci soliton, \emph{Chaos, Solitons \& Fractals} 44(8) (2011), 647-650.
CR  - R. S. Hamilton, Three-manifolds with positive Ricci curvature, \emph{J. Diff. Geom.} 17(2) (1982), 255-306.
CR  - C. He, M. Zhu, The Ricci solitons on Sasakian manifolds, \emph{arxiv:1109.4407v2.} 2011.
CR  - G. Ingalahalli, C. S. Bagewadi, Ricci solitons in $\alpha-$Sasakian manifolds, \emph{ISRN Geometry} vol.2012, Article ID 421384, 13 Pages, (2012).
CR  - M. A. Khan,  M. Z. Khan, Totally umbilical semi-invariant submanifolds of a nearly cosymplectic manifold, \emph{Filomat} 20(2) (2006), 33-38.
CR  - M. E. A. Mekki, A. M. Cherif, Generalised Ricci solitons on Sasakian manifolds, \emph{Kyungpook Math. J.} 57(4) (2017), 677-682.
CR  - A. Mihai and R. Roşça, On a class of Einstein space-time manifolds, \emph{Publ. Math. Debrecen} 67(2005), 471-480.
CR  - H. G. Nagaraja, K. Venu, Ricci solitons in Kenmotsu manifolds, \emph{Journal of Informatic and Mathematical Sciences} 8(1) (2016) 29-36.
CR  - S. Y. Perktaş, S. Keleş, Ricci solitons in 3-dimensional normal almost paracontact metric manifolds, \emph{Int. Electron. J. Geom.} 8(2) (2015), 34-45.
CR  - M. Petroviç, R. Roşça and L. Verstraelen, Exterior concurrent vector fields on Riemannian manifolds. I. some general results, \emph{Soochow J. Math.} 15(1989), 179-187.
CR  - R. Sharma, Certain results on K-contact and $(k,\mu)-$contact manifolds, \emph{J. Geom.} 89, no.1-2 (2008), 138-147.
CR  - R. Sharma, A. Ghosh, Sasakian 3-manifolds as a Ricci soliton represents the Heisenberg group, \emph{Int. J. Geom. Methods Mod. Phys} 8(1) (2011), 149-154.
CR  - M. D. Siddiqi, M. Haseeb, M. Ahmad,  Skew semi-invariant submanifolds of generalized quasi-Sasakian manifolds, \emph{Carpathian Math. Publ.} 9(2) (2017), 188-197.
CR  - M. M. Tripathi, Ricci solitons in contact cetric manifolds, \emph{arXiv:0801.4222v1 [math DG]} (2008).
CR  - K. Yano, Sur le parall\'{e}lisme et la concourance dans l'escape de Riemannian, \emph{Proc. Imp. Acad. Tokyo} 19(1943), 189-197.
CR  - K. Yano,  B.-Y. Chen, On the concurrent vector fields of immersed manifolds, \emph{Kodai Math. Sem. Rep.} 23(1971), 343-350.
CR  - K. Yano, M. Kon, Structures on manifolds, Series in Mathematics, World Scientific Publishing, Springer, (1984).
UR  - https://doi.org/10.31801/cfsuasmas.445788
L1  - https://dergipark.org.tr/en/download/article-file/727443
ER  -