Conformal Metric, Euler Number and Trüdinger Constant on Two-Dimensional Manifolds
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Date
2022
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This thesis calculates the Scalar curvature by expanding Christoffel symbols, so we get the relation about Scalar curvatures under conformal metrics. Then, we classify two-dimension Riemannian manifolds by Euler number and discuss the existence of the conformal metrics in the different Euler numbers. Finally, in the case of χ(M )> 0, we give more details about the Trüdinger constant and see the possibilities for the different Trüdinger constants.
This thesis calculates the Scalar curvature by expanding Christoffel symbols, so we get the relation about Scalar curvatures under conformal metrics. Then, we classify two-dimension Riemannian manifolds by Euler number and discuss the existence of the conformal metrics in the different Euler numbers. Finally, in the case of χ(M )> 0, we give more details about the Trüdinger constant and see the possibilities for the different Trüdinger constants.
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none, Christoffel symbols, Scalar curvatures, Riemannian manifold, Trüdinger constant