Semi-symmetric Metric Connections On Riemannian Manifold

The thesis studies the properties of semi-symmetric metric connec-tions on the Riemannian manifold. It consists of three chapters.In Chapter I, the motivations of our work are introduced. In addition,some preliminary concepts and main results are presented.In Chapter II, first of all, the definitions of semi-symmetric metricconnections on the Riemannian manifold and local coordinates of its ten-sors are introduced. Then the relations among tensors are simplified if thecharacteristic tensor of semi-symmetric metric connections is proportionalto metric tensor of Riemannian connections. Furthermore, new propertiesare derived from the above analysis.In Chapter III, the semi-symmetric recurrent metric connections aredefined. On the basis of fundamental definitions, certain relations amongtensors of semi-symmetric recurrent metric connections are investigated.In addition, some new conclusions are obtained from general connections.