A Study on Ricci Solitons in Generalized Complex Space Form
Palabras clave:
Kähler manifolds, generalized complex space form, parallel second order covariant tensor field, Einstein space, Ricci solitonResumen
In this paper we obtain the condition for the existence of Ricci solitons in non-flat generalized complex space form by using Eisenhart problem. Also it is proved that if (g, V, λ) is Ricci soliton then V is solenoidal if and only if it is shrinking or steady or expanding depending upon the sign of scalar curvature.
Descargas
Referencias
C.S. Bagewadi, G. Ingalahalli, Ricci solitons in Lorentzian α-Sasakian manifolds, Acta Mathematica. Academiae Paedagogicae Nyíregyháziensis 28 (1) (2012), 59 – 68.
C.S. Bagewadi, M.M. Praveena, Semi-symmetric conditions on generalized complex space forms, Acta Math. Univ. Comenian. (N.S.) 85 (1) (2016), 147 – 154.
D.E. Blair, “A Contact Manifolds in Riemannian Geometry”, Lecture Notes in Mathematics, 509, Springer-Verlag, Berlin-New York, 1976.
C. Calin, M. Crasmareanu, From the Eisenhart problem to Ricci solitons in f -Kenmotsu manifolds, Bull. Malays. Math. Sci. Soc. (2) 33 (3) (2010), 361 – 368.
S. Debnath, A. Bhattacharyya, Second order parallel tensor in trans-Sasakian manifolds and connection with Ricci soliton, Lobachevskii Journal of Mathematics 33 (4) (2012), 312 – 316.
L.P. Eisenhart, Symmetric tensors of the second order whose first covariant derivatives are zero, Trans. Amer. Math, Soc. 25 (2) (1923), 297 – 306.
G. Ingalahalli, C. S. Bagewadi, Ricci solitons in α-Sasakian manifolds, ISRN Geometry, Volume 2012 (2012), Article ID 421384, 13 pages.
H. Levy, Symmetric tensors of the second order whose covariant derivatives vanish, Ann. of Math. (2) 27 (2) (1925), 91 – 98.
Z. Olszak, On the existence of generalized complex space forms, Isrel J. Math. 65 (2) (1989), 214 – 218.
M.M. Praveena, C.S. Bagewadi, On almost pseudo Bochner symmetric generalized complex space forms, Acta Mathematica. Academiae Paedagogicae Nyíregyháziensis 32 (1) (2016), 149 – 159.
R. Sharma, Second order parallel tensor in real and complex space forms, Internat. J. Math. and Math. Sci. 12 (4) (1989), 787 – 790.
P. Topping, “Lectures on the Ricci Flow”, London Mathematical Society Lecture Note Series, 325, Cambridge University Press, Cambridge, 2006.