Einstein metrics on a class of five-dimensional homogeneous spaces
We prove that there is exactly one homothety class of invariant Einstein metrics in each space defined below.
On a new family of homogeneous Einstein manifolds
We show that there exists exactly one homothety class of invariant Einstein metrics on each space defined below.
Conformal deformations of the Riemannian metrics and homogeneous Riemannian spaces
In this paper we investigate one-dimensional sectional curvatures of Riemannian manifolds, conformal deformations of the Riemannian metrics and the structure of locally conformally homogeneous Riemannian manifolds. We prove that the nonnegativity of the one-dimensional sectional curvature of a homogeneous Riemannian space attracts nonnegativity of the Ricci curvature and we show that the inverse is incorrect with the help of the theorems O. Kowalski-S. Nikčevi'c [K-N], D. Alekseevsky-B. Kimelfeld...
Standard homogeneous Einstein manifolds and Diophantine equations
Some new examples of standard homogeneous Einstein manifolds with semisimple transitive groups of motions and semisimple isotropy subgroups are constructed. For the construction of these examples the solutions of some systems of Diophantine equations are used.
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