Abstract: In R^n, identifying each direction as point in S^{n-1}, Mattila, in 1975, showed that for any Borel set Z in R^n, the orthogonal projection of Z to H^{n-1} almost every direction has dimension min{Z, 1}. In this talk, we show a restricted projection theorem for all analytic sets Z in R^{n+1} with n >2 : Let M \subset S^n be an (n-1)-dimensional manifold with sectional curvature >1. Then for all analytic sets Z, the orthogonal projection of Z to H^{n-1} almost every direction determined by M has dimension min{Z, 1}.
