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Einstein metrics on rational homology 7-spheres

Charles P. Boyer, Krzysztof Galicki, Michael Nakamaye (2002)

Annales de l’institut Fourier

In this paper we demonstrate the existence of Sasakian-Einstein structures on certain 2- connected rational homology 7-spheres. These appear to be the first non-regular examples of Sasakian-Einstein metrics on simply connected rational homology spheres. We also briefly describe the rational homology 7-spheres that admit regular positive Sasakian structures.

Einstein-Hermitian and anti-Hermitian 4-manifolds

Włodzimierz Jelonek (2003)

Annales Polonici Mathematici

We study 4-dimensional Einstein-Hermitian non-Kähler manifolds admitting a certain anti-Hermitian structure. We also describe Einstein 4-manifolds which are of cohomogeneity 1 with respect to an at least 4-dimensional group of isometries.

Einstein-like semi-symmetric spaces

Eric Boeckx (1993)

Archivum Mathematicum

One proves that semi-symmetric spaces with a Codazzi or Killing Ricci tensor are locally symmetric. Some applications of this result are given.

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