In this paper we generalize a result in [J. An, Z. Wang, On the realization of Riemannian symmetric spaces in Lie groups, Topology Appl. 153 (7) (2005) 10081015, showing that an arbitrary Riemannian symmetric space can be realized as a closed submanifold of a covering group of the Lie group defining the symmetric space. Some properties of the subgroups of fixed points of involutions are also proved.

Let  $\sum$ be a complete minimal Lagrangian submanifold of $\mathbb{C}^n$. We identify regions in the Grassmannian of Lagrangian subspaces so that whenever the image of the Gauss map of $\sum$ lies in one of these regions, then  $\sum$ is an affine space.

We give a complete diffeomorphism classification of 1-connected closed manifolds M with integral homology H¤(M) ∼= Z ⊕ Z ⊕ Z, provided that dim(M) 6= 4.

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