#TITLE_ALTERNATIVE#

• Main Author: NATANAEL WIJAYA (NIM. 20212035)Pembimbing : Dr. rer. nat Bobby Eka Gunara, RIO
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/19332
• Institution: Institut Teknologi Bandung

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 /> <br /> <br /> <br /> <br /> <br /> metric we use is Joyce metric which reduce the selfdual condition from second order <br /> <br /> <br /> <br /> <br /> <br /> <br /> to first order partial diferential equation. These equations is the condition for four <br /> <br /> <br /> <br /> <br /> <br /> <br /> function (A0, A1, B0, and B1) in the metric. The explicit solution is obtained <br /> <br /> <br /> <br /> <br /> <br /> <br /> with the assumption of separation of variables. We also proved that the separation <br /> <br /> <br /> <br /> <br /> <br /> <br /> constant cannot both be zero, for the metric will become singular. The solution <br /> <br /> <br /> <br /> <br /> <br /> <br /> for constant Ricci scalar is obtained after we conformally transformed the metric. <br /> <br /> <br /> <br /> <br /> <br /> <br /> Conformal transformation with scale factor =G2 will results in Calderbank-Pedersen <br /> <br /> <br /> <br /> <br /> <br /> <br /> metic with negative scalar Curvature.