Riemannian manifolds in which certain curvature operator has constant eigenvalues along each helix

Yana Alexieva; Stefan Ivanov

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The property of being a D’Atri space (i.e., a space with volume-preserving symmetries) is equivalent to the infinite number of curvature identities called the odd Ledger conditions. In particular, a Riemannian manifold $(M, g)$ satisfying the first odd Ledger condition is said to be of type $𝒜$ . The classification of all 3-dimensional D’Atri spaces is well-known. All of them are locally naturally reductive. The first attempts to classify all 4-dimensional homogeneous D’Atri spaces were done in...

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