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In general, Whitham dynamics involves infinitely many parameters calledWhitham times, but in the context of N=2 supersymmetric Yang-Mills theory itcan be regarded as a finite system by restricting the number of Whitham timesappropriately. For example, in the case of SU(r+1) gauge theory withouthypermultiplets, there are r Whitham times and they play an essential role inthe theory. In this situation, the generating meromorphic 1-form of the Whithamhierarchy on Seiberg-Witten curve is represented by a finite linear combinationof meromorphic 1-forms associated with these Whitham times, but it turns outthat there are various differential relations among these differentials. Sincethese relations can be written only in terms of the Seiberg-Witten 1-form,their consistency conditions are found to give the Picard-Fuchs equations forthe Seiberg-Witten periods.Comment: to be published in J. Math. Phys, revtex, 14 page

Picard–Fuchs equations and Whitham hierarchy in N=2 supersymmetric SU(r+1) Yang–Mills theory