MEASURE OF LINEAR SPACES AND TOTAL CURVATURES OF COMPACT ANTI-INVARIANT SUBMANIFOLDS IN $\ce^n$. Ximo Gual Arnau Abstract. Let $M$ be a totally real compact manifold, immersed in the Kaehler manifold $\re^{2n}$. We define the total curvatures of $M$ and we get a local interpretation of them. Previously, we obtain an invariant measure for the different linear spaces in $\ce^n$. Keywords. Total curvatures, densities, subspaces in $\ce^n$, moving frames. MS Classification. 53C64.