Open AccessBiharmonic Hypersurfaces of LP-Sasakian Manifolds
Author(s) -
Selcen Yüksel Perktaş,
Erol Kılıç,
Sadık Keleṣ
Publication year - 2011
Publication title -
analele ştiinţifice ale universităţii "al.i. cuza" din iaşi. matematică
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.144
H-Index - 12
eISSN - 2344-4967
pISSN - 1221-8421
DOI - 10.2478/v10157-011-0034-z
Subject(s) - biharmonic equation , hypersurface , vector field , mathematical analysis , manifold (fluid mechanics) , mathematics , pure mathematics , constant (computer programming) , mean curvature , curvature , geometry , boundary value problem , mechanical engineering , programming language , computer science , engineering
Biharmonic Hypersurfaces of LP-Sasakian Manifolds In this paper the biharmonic hypersurfaces of Lorentzian para-Sasakian manifolds are studied. We firstly find the biharmonic equation for a hypersurface which admits the characteristic vector field of the Lorentzian para-Sasakian as the normal vector field. We show that a biharmonic spacelike hypersurface of a Lorentzian para-Sasakian manifold with constant mean curvature is minimal. The biharmonicity condition for a hypersurface of a Lorentzian para-Sasakian manifold is investigated when the characteristic vector field belongs to the tangent hyperplane of the hypersurface. We find some necessary and sufficient conditions for a timelike hypersurface of a Lorentzian para-Sasakian manifold to be proper biharmonic. The nonexistence of proper biharmonic timelike hypersurfaces with constant mean curvature in a Ricci flat Lorentzian para-Sasakian manifold is proved.