In this paper, the existence of a global tangent frame on every oriented and connected smooth 3-manifold will be used to develop a global frame method in 3-dimensional geometry and topology. Corresponding to each glob...In this paper, the existence of a global tangent frame on every oriented and connected smooth 3-manifold will be used to develop a global frame method in 3-dimensional geometry and topology. Corresponding to each global tangent frame, we define a Poisson matrix on the 3-manifold. And using it as an initial date. we give an explicit expression of all the curvatures for some Riemannian metric. The method is well applied to 3-manifolds with constant Poisson matrix. Such 3-manifolds are essentially the homogeneous spaces of 3-dimensional Lie groups.展开更多
文摘In this paper, the existence of a global tangent frame on every oriented and connected smooth 3-manifold will be used to develop a global frame method in 3-dimensional geometry and topology. Corresponding to each global tangent frame, we define a Poisson matrix on the 3-manifold. And using it as an initial date. we give an explicit expression of all the curvatures for some Riemannian metric. The method is well applied to 3-manifolds with constant Poisson matrix. Such 3-manifolds are essentially the homogeneous spaces of 3-dimensional Lie groups.
