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Abstract
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The article describe some recent results about concept of biharmonicity of hypersurfaces in the Sasakian space form, which is equipped with the Tanaka-Webster connection. There is a rich theory whose main message is the necessary and sufficient existence condition of the Tanaka-Webster biharmonic hypersurfaces. Also, it is included a brief nonexistence result of the Tanaka-Webster biharmonic Hopf hypersurfaces, where the gradient of the mean curvature is a principal direction.
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