Some Biharmonic Problems on the Tangent Bundle with a Berger-type Deformed Sasaki Metric

Abstract

Let (M<sub>2k</sub>,Φ,g) be an almost anti-paraKahler manifold and TM its tangent bundle equipped with the Berger type deformed Sasaki metric gBS and the paracomplex structure Φ<sub>˜</sub>. In this paper, we deal with the biharmonicity of canonical projection π : TM →M and a vector field X which is considered as a map X : M → TM.