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We characterize proper biharmonic anti-invariant surfaces in $3$-dimensional generalized $(\kappa, \mu)$-manifolds with constant mean curvature by means of the scalar curvature of the ambient space and the mean curvature. In addition, we give a method for constructing infinity many examples of proper biharmonic submanifolds in a certain $3$-dimensional generalized $(\kappa, \mu)$-manifold. Moreover, we determine $3$-dimensional generalized $(\kappa, \mu)$-manifolds which admit a certain kind of proper biharmonic foliation.
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참고문헌 (12)
참고문헌 신청
K. Arslan / 2005 / Biharmonic submanifolds in 3-dimensional (κ, μ)-manifolds / Int. J. Math. Math. Sci 22(22):3575~3586
D. E. Blair / 1995 / Contact metric manifolds satisfying a nullity condition / Israel J. Math 91(1-3):189~214
R. Caddeo / 2001 / Biharmonic submanifolds of S3 / Internat. J. Math 21(8):867~876
J. Eells / 1983 / Selected topics in harmonic maps / AMS Providence
D. Fetcu / 2007 / Explicit formulas for biharmonic submanifolds in non-Euclidean 3-spheres / Abh. Math. Sem. Univ. Hambg 77:179~190
D. E. Blair / 1995 / Contact metric manifolds satisfying a nullity condition / Israel J. Math 91(1-3):189~214
R. Caddeo / 2001 / Biharmonic submanifolds of S3 / Internat. J. Math 21(8):867~876
J. Eells / 1983 / Selected topics in harmonic maps / AMS Providence
D. Fetcu / 2007 / Explicit formulas for biharmonic submanifolds in non-Euclidean 3-spheres / Abh. Math. Sem. Univ. Hambg 77:179~190
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