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Power corrections for virtual Compton scattering at leading twist areetermined at operator level. From the complete off-cone representation of thetwist-2 Compton operator integral representations for the trace, antisymmetricand symmetric part of that operator are derived. The operator valued invariantfunctions are written in terms of iterated operators and may lead tointerrelations. For matrix elements they go over into relations for generalizedparton distributions. -- Reducing to the s-channel relevant part one getsoperator pre-forms of the Wandzura-Wilczek and the (target mass corrected)Callan-Gross relations whose structure is exactly the same as known from thecase of deep inelastic scattering; taking non-forward matrix elements onereproduces earlier results [B. Geyer, D. Robaschik and J. Eilers, Nucl. Phys. B704 (2005) 279] for the absorptive part of the virtual Compton amplitude. --All these relations, obtained without any approximation or using equations ofmotion, are determined solely by the twist-2 structure of the underlyingoperator and, therefore, are purely of geometric origin.Comment: 13 pages, Latex 2e, Introduction shortend, Section Prerequisites  added, more obvious formulations used, some formulas rewritten as well as  added, conclusions extended, references added. Final version as appearing in  PR

Twist-2 Compton operator and its hidden Wandzura-Wilczek and Callan-Gross structures