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This thesis is about 4-dimensional Riemannian manifold with torus symmetry. We <br /> <br /> <br /> <br /> <br /> <br /> <br /> present the constant Ricci Scalar condition with the assumption of selfduality. The <br /> <br /> <...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/19332 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | This thesis is about 4-dimensional Riemannian manifold with torus symmetry. We <br />
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present the constant Ricci Scalar condition with the assumption of selfduality. The <br />
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metric we use is Joyce metric which reduce the selfdual condition from second order <br />
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to first order partial diferential equation. These equations is the condition for four <br />
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function (A0, A1, B0, and B1) in the metric. The explicit solution is obtained <br />
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with the assumption of separation of variables. We also proved that the separation <br />
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constant cannot both be zero, for the metric will become singular. The solution <br />
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for constant Ricci scalar is obtained after we conformally transformed the metric. <br />
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Conformal transformation with scale factor =G2 will results in Calderbank-Pedersen <br />
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metic with negative scalar Curvature. |
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