In this article, we introduce the sectional curvature in contravariant warped product spaceAfter that we find the sectional curvature of M for which M 1 and M 2 are Poisson manifolds of positive sectional curvatures. In dual space of M , we introduce the notion of null, spacelike, timelike 1− forms and then by using these forms, qualar curvature is defined. Finally, as an examples we obtain the sectional curvatures for M 1 = H 2 1 , M 2 = S 2 0 , E 2 2 and qualar curvature for M .
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