In 2012, MM Graev associated to a compact homogeneous space G/H a nerve XG/H, whose
non-contractibility implies the existence of a G-invariant Einstein metric on G/H. The nerve …

We prove the instability of some families of Riemannian manifolds with non-trivial real Killing
spinors. These include the invariant Einstein metrics on the Aloff-Wallach spaces $ N_ {k …

In the present paper, we review the progress of the project of the classification and
construction of invariant differential operators for non-compact, semisimple Lie groups. Our …

We study existence of invariant Einstein metrics on complex Stiefel manifolds $
G/K=\operatorname {SU}(\ell+ m+ n)/\operatorname {SU}(n) $ and the special unitary groups …

Classification of left-invariant Einstein metrics on $$\textrm{SL}(2,\mathbb {R})\times \textrm{SL}(2,\mathbb
{R})$$ that are bi-invariant under a one-parameter subgroup | Annals of Global Analysis …

We study homogeneous Einstein metrics on indecomposable non-Kähler C-spaces, ie even-
dimensional torus bundles M= G∕ H with rank G> rank H over flag manifolds F= G∕ K of a …

In the present paper, we review the progress of the project of the classification and
construction of invariant differential operators for non-compact, semisimple Lie groups. Our …

We classify all left-invariant pseudo-Riemannian Einstein metrics on $\mathrm
{SL}(2,\mathbb {R})\times\mathrm {SL}(2,\mathbb {R}) $ that are bi-invariant under a one …

1. Background 1.1. Positive Curvature. The relationship between geometry and topology has
fascinated mathematicians throughout the history of mathematical research. In particular …

In this report we summarize the research in mathematics and theoretical physics done in
project A6 of the SFB 676. The main research directions include the study of internal spaces …