Poisson Matrices on 3-Manifolds and Their Applications to 3-CPM Manifolds |
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Authors: | Hong Jun Li |
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Affiliation: | (1) Science School, Xi'an Jiaotong University, Xi'an 710049, P. R. China |
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Abstract: | 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. |
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Keywords: | Global frames Poisson matric Curvature 3-CPM manifolds Homogeneous spaces |
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