The object of the present paper is to introduce the notion of generalized φ-recurrent Sasakian manifold and study its various geometric properties with the existence of such notion. Among others we study generalized ...The object of the present paper is to introduce the notion of generalized φ-recurrent Sasakian manifold and study its various geometric properties with the existence of such notion. Among others we study generalized concircularly φ-recurrent Sasakian manifolds. The existence of generalized φ-recurrent Sasakian manifold is given by a proper example.展开更多
This paper deals with the study of CR-submanifolds of a nearly trans-Sasakian manifold with a semi symmetric non-metric connection. Nijenhuis tensor, integrability conditions for some distributions on CR-submanifolds ...This paper deals with the study of CR-submanifolds of a nearly trans-Sasakian manifold with a semi symmetric non-metric connection. Nijenhuis tensor, integrability conditions for some distributions on CR-submanifolds of a nearly trans-Sasakian manifold with a semi symmetric non- metric connection are discussed.展开更多
In this paper, we study geodesic contact CR-lightlike submanifolds and geodesic screen CR-lightlike (SCR) submanifolds of indefinite Sasakian manifolds. Some necessary and sufficient conditions for totally geodesic, m...In this paper, we study geodesic contact CR-lightlike submanifolds and geodesic screen CR-lightlike (SCR) submanifolds of indefinite Sasakian manifolds. Some necessary and sufficient conditions for totally geodesic, mixed geodesic, -geodesic and -geodesic contact CR-lightlike submanifolds and SCR submanifolds are obtained.展开更多
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
The authors consider a quarter-symmetric metric connection in a P-Sasakian manifold and study the second order parallel tensor in a P-Sasakian manifold with respect to the quarter-symmetric metric connection. Then Ric...The authors consider a quarter-symmetric metric connection in a P-Sasakian manifold and study the second order parallel tensor in a P-Sasakian manifold with respect to the quarter-symmetric metric connection. Then Ricci semisymmetric P-Sasakian manifold with respect to the quarter-symmetric metric connection is considered. Next the authors study ξ-concircularly flat P-Sasakian manifolds and concircularly semisymmetric P-Sasakian manifolds with respect to the quarter-symmetric metric connection. Furthermore, the authors study P-Sasakian manifolds satisfying the condition Z(ξ,Y)·S=0,where Z,S are the concircular curvature tensor and Ricci tensor respectively with respect to the quarter-symmetric metric connection. Finally, an example of a 5-dimensional P-Sasakian manifold admitting quarter-symmetric metric connection is constructed.展开更多
文摘The object of the present paper is to introduce the notion of generalized φ-recurrent Sasakian manifold and study its various geometric properties with the existence of such notion. Among others we study generalized concircularly φ-recurrent Sasakian manifolds. The existence of generalized φ-recurrent Sasakian manifold is given by a proper example.
文摘This paper deals with the study of CR-submanifolds of a nearly trans-Sasakian manifold with a semi symmetric non-metric connection. Nijenhuis tensor, integrability conditions for some distributions on CR-submanifolds of a nearly trans-Sasakian manifold with a semi symmetric non- metric connection are discussed.
文摘In this paper, we study geodesic contact CR-lightlike submanifolds and geodesic screen CR-lightlike (SCR) submanifolds of indefinite Sasakian manifolds. Some necessary and sufficient conditions for totally geodesic, mixed geodesic, -geodesic and -geodesic contact CR-lightlike submanifolds and SCR submanifolds are obtained.
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supported by the National Natural Science Foundation of China(Nos.11871275,11371194).
文摘The authors consider a quarter-symmetric metric connection in a P-Sasakian manifold and study the second order parallel tensor in a P-Sasakian manifold with respect to the quarter-symmetric metric connection. Then Ricci semisymmetric P-Sasakian manifold with respect to the quarter-symmetric metric connection is considered. Next the authors study ξ-concircularly flat P-Sasakian manifolds and concircularly semisymmetric P-Sasakian manifolds with respect to the quarter-symmetric metric connection. Furthermore, the authors study P-Sasakian manifolds satisfying the condition Z(ξ,Y)·S=0,where Z,S are the concircular curvature tensor and Ricci tensor respectively with respect to the quarter-symmetric metric connection. Finally, an example of a 5-dimensional P-Sasakian manifold admitting quarter-symmetric metric connection is constructed.
