In this paper we study a class of metrics with some compatible almost complex structures on the tangent bundle TM of a Riemannian manifold (M,g), which are parallel to those in [10]. These metrics generalize the class...In this paper we study a class of metrics with some compatible almost complex structures on the tangent bundle TM of a Riemannian manifold (M,g), which are parallel to those in [10]. These metrics generalize the classical Sasaki metric and Cheeger-Gromoll metric. We prove that the tangent bundle TM endowed with each pair of the above metrics and the corresponding almost complex structures is a locally conformal almost K¨ahler manifold. We also find that, when restricted to the unit tangent sphere bundle, these metrics and corresponding almost complex structures define new examples of contact metric structures.展开更多
基金the National Natural Science Foundation of China (No.10671181)
文摘In this paper we study a class of metrics with some compatible almost complex structures on the tangent bundle TM of a Riemannian manifold (M,g), which are parallel to those in [10]. These metrics generalize the classical Sasaki metric and Cheeger-Gromoll metric. We prove that the tangent bundle TM endowed with each pair of the above metrics and the corresponding almost complex structures is a locally conformal almost K¨ahler manifold. We also find that, when restricted to the unit tangent sphere bundle, these metrics and corresponding almost complex structures define new examples of contact metric structures.
