The idea of this research is to study different types of connections in an almost Hermite manifold. The connection has been established between linear connection and Riemannian connection. Three new linear connections...The idea of this research is to study different types of connections in an almost Hermite manifold. The connection has been established between linear connection and Riemannian connection. Three new linear connections <span style="white-space:nowrap;">∇</span><sup>1</sup>, <span style="white-space:nowrap;">∇</span><sup>2</sup>, <span style="white-space:nowrap;">∇</span><sup>3</sup> are introduced. The necessary and sufficient condition for <span style="white-space:nowrap;">∇</span><sup>1</sup>, <span style="white-space:nowrap;">∇</span><sup>2</sup>, <span style="white-space:nowrap;">∇</span><sup>3</sup> to be metric is discussed. A new metric <i>s</i><sup>*</sup> (<i>X</i>,<i>Y</i>) has been defined for (<i>M</i><sup><i>n</i></sup>,<i>F</i>,<i>g</i><sup>*</sup>) and additional properties are discussed. It is also proved that for the quarter symmetric connection <span style="white-space:nowrap;">∇ </span>is unique in given manifold. The hessian operator with respect to all connections defined above has also been discussed.展开更多
The conjugate of T-connection in a Riemannian manifold is obtained, also some of its properties are studied. T-statistical manifold is defined and was considered. Finally a characteristic vector field of the deformati...The conjugate of T-connection in a Riemannian manifold is obtained, also some of its properties are studied. T-statistical manifold is defined and was considered. Finally a characteristic vector field of the deformation algebra （M, , ） is also obtained.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 idea of this research is to study different types of connections in an almost Hermite manifold. The connection has been established between linear connection and Riemannian connection. Three new linear connections <span style="white-space:nowrap;">∇</span><sup>1</sup>, <span style="white-space:nowrap;">∇</span><sup>2</sup>, <span style="white-space:nowrap;">∇</span><sup>3</sup> are introduced. The necessary and sufficient condition for <span style="white-space:nowrap;">∇</span><sup>1</sup>, <span style="white-space:nowrap;">∇</span><sup>2</sup>, <span style="white-space:nowrap;">∇</span><sup>3</sup> to be metric is discussed. A new metric <i>s</i><sup>*</sup> (<i>X</i>,<i>Y</i>) has been defined for (<i>M</i><sup><i>n</i></sup>,<i>F</i>,<i>g</i><sup>*</sup>) and additional properties are discussed. It is also proved that for the quarter symmetric connection <span style="white-space:nowrap;">∇ </span>is unique in given manifold. The hessian operator with respect to all connections defined above has also been discussed.
文摘The conjugate of T-connection in a Riemannian manifold is obtained, also some of its properties are studied. T-statistical manifold is defined and was considered. Finally a characteristic vector field of the deformation algebra （M, , ） is also obtained.
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.
