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Biharmonic Curves in Lorentzian Para-Sasakian Manifolds
(Malaysian Mathematical Sciences Soc, 2010) Keles, Sadik; Perktas, Selcen Yueksel; Kilic, Erol
In this paper we give necessary and sufficient conditions for space-like and timelike curves in a conformally fiat, quasi conformally flat and conformally symmetric 4-dimensional Lorentzian Para-Sasakian (LP-Sasakian) manifold to be proper biharmonic. Also, we investigate proper biharmonic curves in the Lorentzian sphere S-1(4).
Biharmonic maps between doubly warped product manifolds
(Balkan Soc Geometers, 2010) Perktas, Selcen Yueksel; Kilic, Erol
In this paper biharmonic maps between doubly warped product manifolds are studied. We show that the inclusion maps of Riemannian manifolds Band F into the nontrivial (proper) doubly warped product manifold (f)B x(b) F cannot be proper biharmonic maps. Also we analyze the conditions for the biharmonicity of projections (f)B x(b) F -> B and (f)B x(b) F -> F, respectively. Some characterizations for non-harmonic biharmonic maps are given by using product of harmonic maps and warping metric. Especially, in the case of f = 1, the results for warped product in [4] are obtained.