论文标题
四分之一对称的非金属连接
Quarter-symmetric non-metric connection
论文作者
论文摘要
该论文将在普通的里曼尼亚歧管上研究新的四分之一对称的非金属连接。它将决定扭转张量满足的关系。 The exterior derivative of the skew-symmetric part $F$ of basic tensor $G$ with respect to the Levi-Civita connection coincides with that of skew-symmetric part $F$ with respect to quarter-symmetric non-metric connection, which implies that the even-dimensional manifold endowed with $F$ is symplectic manifold if and only if it is closed with respect to quarter-symmetric non-metric connection.确定了该连接的线性独立曲率张量及其双重连接，并讨论了这些张量的性能。最后，条件是连接应为双对称。
The paper will study a new quarter-symmetric non-metric connection on a generalized Riemannian manifold. It will determine the relations that the torsion tensor satisfies. The exterior derivative of the skew-symmetric part $F$ of basic tensor $G$ with respect to the Levi-Civita connection coincides with that of skew-symmetric part $F$ with respect to quarter-symmetric non-metric connection, which implies that the even-dimensional manifold endowed with $F$ is symplectic manifold if and only if it is closed with respect to quarter-symmetric non-metric connection. The linearly independent curvature tensors of this connection and its dual connection are determined and the properties of these tensors are discussed. Finally, the condition is given that the connection should be dual symmetric.
