content_image/337417.jpg content_image/337418.jpg content_image/337419.jpg content_image/337420.jpg content_image/337421.jpg content_image/337422.jpg content_image/337423.jpg content_image/337424.jpg content_image/337425.jpg
Here we want to obtain the ( n + 1)-dimensional static solutions of Eqs. (3), (4) and (5). We assume that the metric has the following form 

where 

represents the line element of an ( n − 1)-dimensional hypersurface with constant curvature ( n − 1)( n − 2) k . It is notable that positive curvature horizon ( k = 1) has been investigated in [29]. Here N ( ρ ), f ( ρ ) and R ( ρ ) are functions of ρ which should be determined. First of all, the Maxwell equations (5) can be integrated immediately, where all the components of F$_{µν}$ are zero except F$_{tρ}$ 

<img src='content_image/337417.jpg'>

<img src='content_image/337418.jpg'>

<img src='content_image/337419.jpg'>

where q , an integration constant, is the charge parameter of the black brane. Our aim here is to construct exact, ( n + 1)-dimensional topological AdS black brane solutions of Eqs. (3)-(5), with the dilaton potential (2) for an arbitrary dilaton coupling parameter α and investigate their properties. Using metric (6) and the Maxwell field (7), one can show that the system of equations (3)-(4) have solutions of the form 

Here c and b are integration constants and the constant γ is 

The charge parameter q is related to b and c by 

<img src='content_image/337420.jpg'>

<img src='content_image/337421.jpg'>

<img src='content_image/337422.jpg'>

<img src='content_image/337423.jpg'>

<img src='content_image/337424.jpg'>

<img src='content_image/337425.jpg'>

