Abstract In this article, we study the stability problem for Einstein–Hilbert functional on compact symmetric spaces following and completing seminal work of Koiso subject. We classify in detail irreducible representations simple Lie algebras with Casimir eigenvalue less than adjoint representation use information to prove Einstein metrics both quaternionic Cayley projective plane. Moreover, th...

We prove $L^{p}$-boundedness of oscillating multipliers on some classes rank one locally symmetric spaces.

We obtain explicit formulas for the rational homotopy groups of generalised symmetric spaces, i.e., the homogeneous spaces for which the isotropy subgroup appears as the fixed point group of some finite order automorphism of the group. In particular, this gives explicit formulas for the rational homotopy groups of all classical compact symmetric spaces.

We study the L-spectrum of the Laplace-Beltrami operator on certain complete locally symmetric spaces M = Γ\X with finite volume and arithmetic fundamental group Γ whose universal covering X is a symmetric space of non-compact type. We also show, how the obtained results for locally symmetric spaces can be generalized to manifolds with cusps of rank one.

We classify homogeneous Einstein metrics on compact irreducible symmetric spaces. In particular, we consider symmetric spaces with rank(M) > 1, not isometric to a compact Lie group. Whenever there exists a closed proper subgroup G of Isom(M) acting transitively on M we nd all G-homogeneous (non-symmetric) Einstein metrics on M .