In this work, we study the existence of invariant almost complex structures on real flag manifolds associated to split real forms of complex simple Lie algebras. We show that, contrary to the complex case where the invariant ...

In this paper we obtain obstructions to the existence of Einstein metrics satisfying auxiliary sectional curvature bounds. In particular, we give sufficient conditions for a compact-oriented Einstein four-manifold M to be ...

Let G(k,n) be the complex Grassmann manifold of k-planes in Ck+n. In this note, we show that for 1 < k < n and for any selfmap f: G(k,n) → G(k,n), there exists a k-plane Vk ∈ G(k,n) such that f(Vk) ∩ Vk ≠ {0}.

In this paper we study functions and vector fields with isolated singularities on a C(ℂPn)-singular manifold. In general, a C(ℂPn)-singular manifold is obtained from a smooth (2n + 1)-manifold with boundary which is a ...

On a product manifold (M, r), we consider four geometric structures compatible with r, e.g. hyper-paracomplex or bi-Lagrangian, and define distinguished generalized complex or paracomplex structures on M, which interpolate ...

Let S be a subsemigroup with nonempty interior of a connected complex simple Lie group G. It is proved that S = G if S contains a subgroup G (α) ≈ Sl (2, C) generated by the exp g±α, where gα is the root space of the root ...