ON THE SECTIONAL CURVATURE OF A RIEMANNIAN MANIFOLD

In this paper the author establishes the following 1.If M~n(n≥3)is a connected Riemannian manifold,then the sectional curvature K(p),where p is any plane in T~x(M),is a function of at most n(n-1)/2 variables.More precisely,K(p)depends on at most n(n-1)/2 parameters of group SO(n). 2.Lot M~n(n≥3)be a connected Riemannian manifold.If there exists a point x ∈ M such that the sectional curvature K(p)is independent of the plane p∈T_x(M),then M is a space of constant curvature. This latter improves a well-known theorem of F.Schur.