Let k(S^2_q) be the "coordinate ring" of a quantum sphere. We introduce the cotangent module on the quantum sphere as a one-sided k(S^2_q)-module and show that there is no Yang-Baxter type operator converting it into a k(S^2_q)-bimodule which would be a flatly deformed object w.r.t. its classical counterpart. This implies non-flatness of any covariant differential calculus on the quantum sphere making use of the Leibniz rule. Also, we introduce the cotangent and tangent modules on generic

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... m orbits and discuss some related problems of "braided geometry".