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 A short note on biharmonic submanifolds in 3-dimensional generalized $(\kappa, \mu)$-manifolds Bull. Korean Math. Soc. 2016 Vol. 53, No. 3, 723-732 https://doi.org/10.4134/BKMS.b150275Published online May 31, 2016 Toru Sasahara Hachinohe Institute of Technology Abstract : 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. Keywords : biharmonic submanifolds, Legendre curves, anti-invariant surfaces, generalized $(\kappa, \mu)$-manifolds MSC numbers : Primary 53C42; Secondary 53B25 Downloads: Full-text PDF