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In this paper, we study the defocusing cubic Schr\"{o}dinger equation onthree dimensional hyperbolic space $\mathbb{H}^3$ with radial initial data inthe Sobolev Space $H^s(0<s<1)$. Our main result is that the initial valueproblem is globally wellposed and scatters for $\frac{15}{16}<s<1$. This is anextension of the work of Staffilani and Yu to the three dimensional hyperbolicspace.

A Scattering Result of the Radial Cubic Defocusing Schr\"odinger Equation on the 3d Hyperbolic Space