Biharmonic submanifolds in non-Sasakian contact metric 3-manifolds

Abstract

In this paper, we characterize biharmonic Legendre curves in 3-dimensional (κ, μ, ν)-contact metric manifolds. Moreover, we give examples of Legendre geodesics in these spaces. We also give a geometric interpretation of 3-dimensional generalized (κ, μ)-contact metric manifolds in terms of its Legendre curves. Furthermore, we study biharmonic anti-invariant surfaces of 3-dimensional generalized (κ, μ)-contact metric manifolds with constant norm of the mean curvature vector field. Finally, we give examples of anti-invariant surfaces with constant norm of the mean curvature vector field immersed in these spaces.