= Solution
At any point choose orthonormal coordinates. The antisymmetries and pair symmetry of the <Riemann curvature tensor> leave only $R_{1212}$ independent. In these coordinates,
$$
R_{11}=R_{1212},\qquad
R_{22}=R_{1212},\qquad
R_{12}=0,
$$
while $R=2R_{1212}$. Since this is a tensor identity, it follows in every coordinate system that the <Ricci tensor in two dimensions> satisfies
$$
\boxed{R_{\alpha\beta}=\frac12g_{\alpha\beta}R}.
$$
The <Einstein tensor> consequently vanishes identically. Hence the two-dimensional vacuum field equation contains no local gravitational dynamics, while coupling the unmodified equation to matter would require $T_{\alpha\beta}=0$. This is the basic degeneracy of <two-dimensional general relativity>.
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