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<p>Multidimensional space-times are represented as curved surfaces embedded in higher dimensional flat spaces. The embedding of each surface is based on geometrical principles. According to these geometrical principles, we use variable separated coordinates so that the coordinates parameters become an orthogonal curved coordinates system for each space-time surface. In this way, we obtain that the universe expands and that the expansion is accelerated. By using co-moving coordinates and assuming that there is at least one geodesic which represent a straight line in the curved multidimensional space-time surface (this is a kind of "equivalence principle" of a new type), we obtain the curved multidimensional space-time surface's equation, its metric and accelerated expanded three-sphere surface's particles that also explains the accelerated expansion of the universe.</p

Geometrical Correlation between Extra-dimensions and Universe Accelerated Expansion