A universal lower bound for the first positive eigenvalue of the Dirac operator on a compact quaternionic Kähler manifold M of positive scalar curvature is calculated. It is shown that it is equal to the first positive eigenvalue on the quaternionic projective space. For this, the horizontal tangent bundle on the canonical SO(3)-bundle over M is equipped with a hyperkählerian structure and the ...

In this paper, we give a complete classification of real hypersurfaces in a quaternionic projective space QPm with ⊥-recurrent second fundamental tensor under certain condition on the orthogonal distribution .

We define in the setting of homotopy type theory an H-space structure on S3. Hence we obtain a description of the quaternionic Hopf fibration S3 ↪→ S7 S4, using only homotopy invariant tools.

The moduli space of the Calabi-Yau three-folds, which play a role as superstring ground states, exhibits the same special geometry that is known from nonlinear sigma models in N = 2 supergravity theories. We discuss the symmetry structure of special real, complex and quaternionic spaces. Maps between these spaces are implemented via dimensional reduction. We analyze the emergence of extra and h...