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