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Osserman manifolds and Weyl-Schouten Theorem for rank-one symmetric spaces
Y. Nikolayevsky
A Riemannian manifold is called Osserman (conformally Osserman, respectively), if the eigenvalues of the Jacobi operator of its curvature tensor (Weyl tensor, respectively) are con…
Conformally Osserman manifolds
Yuri Nikolayevsky
An algebraic curvature tensor is called Osserman if the eigenvalues of the associated Jacobi operator are constant on the unit sphere. A Riemannian manifold is called conformally O…
Einstein solvmanifolds attached to two-step nilradicals
Y. Nikolayevsky
A Riemannian Einstein solvmanifold (possibly, any noncompact homogeneous Einstein space) is almost completely determined by the nilradical of its Lie algebra. A nilpotent Lie algeb…
Einstein solvmanifolds and the pre-Einstein derivation
Y. Nikolayevsky
An Einstein nilradical is a nilpotent Lie algebra, which can be the nilradical of a metric Einstein solvable Lie algebra. The classification of Riemannian Einstein solvmanifolds (p…
Einstein solvmanifolds with a simple Einstein derivation
Y. Nikolayevsky
The structure of a solvable Lie groups admitting an Einstein left-invariant metric is, in a sense, completely determined by the nilradical of its Lie algebra. We give an easy-to-ch…
Osserman Conjecture in dimension n \ne 8, 16
Y. Nikolayevsky
Let M be a Riemannian manifold and R its curvature tensor. For a unit vector X tangent to M at a point p, the Jacobi operator is defined by R_X = R(X, .) X$. The manifold M is call…