The authors consider ±（Φ, J）-holomorphic maps from Sasakian manifolds into Koihler manifolds, which can be seen as counterparts of holomorphic maps in Kiihler ge- ometry. It is proved that those maps must be h...The authors consider ±（Φ, J）-holomorphic maps from Sasakian manifolds into Koihler manifolds, which can be seen as counterparts of holomorphic maps in Kiihler ge- ometry. It is proved that those maps must be harmonic and basic. Then a Schwarz lemma for those maps is obtained. On the other hand, an invariant in its basic homotopic class is obtained. Moreover, the invariant is just held in the class of basic maps.展开更多
The homotopy connectedness theorem for invariant immersions in Sasakian manifolds with nonnegative transversal q-bisectional curvature is proved. Some Barth-Lefschetz type theorems for minimal submanifolds and （k,ε...The homotopy connectedness theorem for invariant immersions in Sasakian manifolds with nonnegative transversal q-bisectional curvature is proved. Some Barth-Lefschetz type theorems for minimal submanifolds and （k,ε）-saddle submanifolds in Sasakian manifolds with positive transversal q-Ricci curvature are proved by using the weak （ε-）asymptotic index. As a corollary, the Frankel type theorem is proved.展开更多
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, th...展开更多
基金supported by the National Natural Science Foundation of China(Nos.10771188,10831008,11071212,11171297)the Doctoral Program Foundation of the Ministry of Education of China(No.20060335133)
文摘The authors consider ±（Φ, J）-holomorphic maps from Sasakian manifolds into Koihler manifolds, which can be seen as counterparts of holomorphic maps in Kiihler ge- ometry. It is proved that those maps must be harmonic and basic. Then a Schwarz lemma for those maps is obtained. On the other hand, an invariant in its basic homotopic class is obtained. Moreover, the invariant is just held in the class of basic maps.
文摘The homotopy connectedness theorem for invariant immersions in Sasakian manifolds with nonnegative transversal q-bisectional curvature is proved. Some Barth-Lefschetz type theorems for minimal submanifolds and （k,ε）-saddle submanifolds in Sasakian manifolds with positive transversal q-Ricci curvature are proved by using the weak （ε-）asymptotic index. As a corollary, the Frankel type theorem is proved.
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, th...
