Ricci solitons on para-Kähler manifolds
Palabras clave:
Para-Kähler manifold, Ricci soliton, pseudosymmetry, paraholomorphic projective curvature, quasi-conformal curvatureResumen
The main purpose of the paper is to study the nature of Ricci soliton on para-Kähler manifolds satisfying some certain curvature conditions. In particular, if we consider certain pseudosymmetric and parallel symmetric tensor on para-Kähler manifolds we prove that V is solenoidal if and only if it is shrinking or steady or expanding depending upon the sign of scalar curvature for dimension M > 4, where (g, V, λ) be a Ricci soliton in a paraholomorphic projectively, pseudosymmetric para-Kähler manifolds. Moreover, we obtain some results related to the quasi-conformal curvature tensor on such manifolds.
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Referencias
K. Amur, Y.B. Maralabhavi, On quasi-conformally flat spaces, Tensor (N.S.) 31 (1977), 194 – 198.
E. Boeckx, O. Kowalski, L. Vanhecke, “ Riemannian Manifolds of Conullity two ”, World Scientific Publication Co., Inc., River Edge, NJ, 1996.
V. Cruceanu, P. Fortuny, P.M. Gadea, A survey on paracomplex geometry, Rocky Mountain J. Math. 26 (1996), 83 – 115.
R. Deszcz, On pseudosymmetric spaces, Bull. Soc. Math. Belg. Sér. A 44 (1992), 1 – 34.
F. Defever, R. Deszcz, L. Verstraelen, On semisymmetric para-Kähler manifolds, Acta Math. Hungar. 74 (1997), 7 – 17.
L.P. Eisenhart, “ Riemannian Geometry ”, Princeton University Press, Princeton, N.J., 1949.
D. Luczyszyn, On para-Kählerian manifolds with recurrent paraholomorphic projective curvature, Math. Balkanica (N.S.) 14 (2000), 167 – 176.
M. Prvanovic, Holomorphically projective transformations in a locally product space, Math. Balkanica 1 (1971), 195 – 213.
E. Reyes, A. Montesinos, P.M. Gadea, Projective torsion and curvature, axiom of planes and free mobility for almost-product manifolds, Ann. Polon. Math. 48 (1988), 307 – 330.
R. Sharma, Second order parallel tensor in real complex space forms, Internat. J. Math. Math. Sci. 12 (1989), 787 – 790.
Z.I. Szabo, Structure theorems on Riemannian spaces satisfying R(X, Y )·R = 0, I, The local version, J. Differential Geom. 17 (1982), 531 – 582.
Z.I. Szabo, Structure theorems on Riemannian spaces satisfying R(X, Y )·R = 0, II, Global version, Geom. Dedicata 19 (1985), 65 – 108.
P. Topping, “ Lectures on the Ricci flow ”, London Mathematical Society Lecturer Note Series, 325, Cambridge University Press, Cambridge, 2006.
K. Yano, S. Sawaki, Riemannian manifolds admitting a conformal transformation group, J. Differential Geometry 2 (1968), 161 – 184.
