Abstract
By considering the p-brane motion in a G/K symmetric space bulk we identify the G-invariant bulk metric in the solvable Lie algebra gauge of the brane action. After calculating the Levi-Civita connection of this bulk metric we use it in the Gauss equation to compute the braneworld curvature in terms of the bulk coordinates. Finally, by making use of the Gauss equation in the braneworld Einstein equation we present a geometrical method of implementing the first fundamental form in the gravitating brane dynamics for the specially chosen symmetric space bulk case leading to an Einstein equation expressed solely in terms of the bulk coordinates of the braneworld.
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