• THE OSSERMAN SURFACES

Prof. Dr. Sci., VESELIN TOTEV VIDEV*

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 Мp, 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.


Keywords


Jacobi operator, hyper surface, pointwise Osserman, Weingarten operator, locally Euclidean hyper surface, hyper sphere.

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