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 d Ω 2 n − 1 =     dθ 2 1 + sinh 2 θ$_{1}$dθ 2 + sinh 2 θ$_{1}$ n − 1 ∑ i =3 i − 1 ∏ j =2 sin 2 θ$_{j}$dθ 2 i k = − 1 n − 1 ∑ i =1 dφ 2 i k = 0 n ds 2 = − N $^{2}$( ρ ) f $^{2}$( ρ ) dt 2 + dρ 2 f $^{2}$( ρ ) + ρ $^{2}$R$^{2}$( ρ ) d Ω 2 n − $_{1}$, (6) F$_{tρ}$ = N ( ρ ) qe 4 α Φ / ( n − 1) ( ρR ) n − 1 , (7) N $^{2}$( ρ ) = Υ − γ ( n − $^{3)}$, (8) f $^{2}$( ρ ) = ρ 2 l 2 Υ ( n − 2) γ + [ k − ( c ρ ) n − 2 ] Υ 1 − $^{γ}$, (9) Φ( ρ ) = n − 1 4 √ γ (2 + 2 γ − nγ ) ln Υ , (10) R $^{2}$( ρ ) = Υ $^{γ}$, (11) Υ = 1 − ( b ρ ) n − 2 . γ = 2 α 2 ( n − 2)( n − 2 + α $^{2}$) . (12) q 2 = ( n − 1)( n − 2) 2 2( n − 2 + α $^{2}$) c n − $^{2}$b n − $^{2}$. (13) Here c and b are integration constants and the constant γ is The charge parameter q is related to b and c by 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 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$_{tρ}$ 5