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High Quality Content by WIKIPEDIA articles! In differential geometry, a Sasakian manifold is a contact manifold (M, ) equipped with a special kind of Riemannian metric g, called a Sasakian metric.Differential geometry is a mathematical discipline that uses the methods of differential and integral calculus, as well as linear and multilinear algebra, to study problems in geometry. The theory of plane and space curves and of surfaces in the three-dimensional Euclidean space formed the basis for its initial development in the eighteenth and nineteenth century. Since the late nineteenth century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds. It is closely related to differential topology, and to the geometric aspects of the theory of differential equations.