Abstract In this paper we study the rotationally invariant harmonic cohomology of a two-parameter family Einstein metrics g which admits cohomogeneity one action SU (2) × U (1) and has AdS asymptotics. Depending on values parameters, is either NUT type, if fixed-point locus zero-dimensional, or bolt it two-dimensional. We find that type then space (2)-invariant two-forms three-dimensional consi...

We study symmetry properties of quaternionic K\"ahler manifolds obtained by the HK/QK correspondence. To any Lie algebra $\mathfrak{g}$ infinitesimal automorphisms initial hyper-K\"ahler data we associate a central extension $\mathfrak{g}$, acting resulting manifold. More specifically, metrics one-loop deformation $c$-map construction, proving that projective special manifold gives rise to Kill...

We study the Lie algebra of infinitesimal isometries on compact Sasakian and K–contact manifolds. On a Sasakian manifold which is not a space form or 3– Sasakian, every Killing vector field is an infinitesimal automorphism of the Sasakian structure. For a manifold with K–contact structure, we prove that there exists a Killing vector field of constant length which is not an infinitesimal automor...

We clarify the global geometry of two 1-parameter families cohomogeneity one Spin(7) holonomy metrics with generic orbit Aloff–Wallach space $$N(1,-1) \cong \text {SU}(3)/\text {U}(1)$$ and singular orbits $$S^5$$ $${\mathbb {C}}P^{2}$$ , which at short distance were shown to exist by Reidegeld. The fit into geography previously known exceptional provide a analogue well-known conifold transitio...

In the Landau–de Gennes theory of liquid crystals, the propensities for alignments of molecules are represented at each point of the fluid by an element Q of the vector space S0 of 3 × 3 real symmetric traceless matrices, or Q-tensors. According to Longa and Trebin [25], a biaxial nematic system is called soft biaxial if the tensor order parameter Q satisfies the constraint tr(Q) = const. After...