Abstract
Let (M, g) be an n-dimensional Riemannian manifold with curvature tensor R and let R X (U) = R U X X = R (U, X, X) be the Jacobi operator defined for a unit tangent vector X in the tangent space M p at a point \( p\in M \). In the present note by a pointwise conditions on the trace and the determinant of R X we characterize locally any classes of a three- and four-dimensional Riemannian manifolds more exactly a spaces of constant sectional curvature, foliated manifolds and a reducible spaces.
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