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Keywords:
tangent bundles; locally conformal hyper-Kähler structures; almost contact metric 3-structures; Sasakian 3-structures
tangent bundles; locally conformal hyper-Kähler structures; almost contact metric 3-structures; Sasakian 3-structures
Summary:
Let $(M,g,J)$ be an almost Hermitian manifold, then the tangent bundle $TM$ carries a class of naturally defined almost hyper-Hermitian structures $(G,J_1,J_2,J_3)$. In this paper we give conditions under which these almost hyper-Hermitian structures $(G,J_1,J_2,J_3)$ are locally conformal hyper-Kähler. As an application, a family of new hyper-\kr structures is obtained on the tangent bundle of a complex space form. Furthermore, by restricting these almost hyper-Hermitian structures on the unit tangent sphere bundle $T_1 M$, we obtain a class of almost contact metric 3-structures. By virtue of these almost contact metric 3-structures, we find a family of Sasakian 3-structures on the unit tangent sphere bundle of a complex space form of positive holomorphic sectional curvature.
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