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Necessary and Sufficient Conditions for the Existence of Metric in Two-Dimensional Affine Manifolds
並列摘要
Necessary and sufficient conditions for the existence of metric in two-dimensional affine manifolds are found to be (i) R12=R21 (ii) R112^1 R112^2; 1=R112^2 R112^1; 1 (iii) R112^1 R112^2; 2=R112^2 R112^1; 2 (iv) R112^1 R212^1; 1=R212^1 R112^1; 1 (v) R112^1 R212^1; 2=R212^1 R112^1; 2, where Rβγδ^τ and Rβδ are respectively the Riemann tensor and the Ricci tensor of the manifold. In case the above five conditions are satisfied, the solutions for metric are found.
並列關鍵字
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