• THE OSSERMAN SURFACES

Abstract

A hyper surface MÌRⁿ⁺¹ is  pointwise Osserman surface if the eigenvalues of the Jacobi operator J(X)= R(u,X,X), where R is the curvature tensor of M, are  pointwise constants, for any tangent vector X in the tangent space М_p, at any point pÎМ. In this short note we prove that M is Osserman surface if and only if M is locally Euclidean hyper surface or hyper surface of constant sectional curvature.