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...

A bstract We present a new infinite family of Type IIB supergravity solutions preserving eight supercharges. The structure the space is AdS 2 × S CY 1 fibered over an interval. These can be related through double analytical continuations with those recently constructed in [1]. Both types are however dual to very different superconformal quantum mechanics. show that our fit locally class 2d Riem...

In this article, we construct two continuous 1-parameter family of non-compact $$\mathrm {Spin}(7)$$ metrics with both chiralities, the principal orbit an Aloff–Wallach space $$N_{k,l}$$ and singular $${{\mathbb {C}}}{{\mathbb {P}}}^2$$ . For a generic , constructed are locally asymptotically conical (ALC). $$N_{1,1}$$ families geometric transition from (AC) to ALC metrics.

In this article, we construct non-compact complete Einstein metrics on two infinite series of manifolds. The first manifolds are vector bundles with $\mathbb{S}^{4m+3}$ as principal orbit and $\mathbb{HP}^{m}$ singular orbit. second $\mathbb{R}^{4m+4}$ the same For each case, a continuous 1-parameter family Ricci-flat 2-parameter negative constructed. particular, $\mathrm{Spin}(7)$ $\mathbb{A}_...

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...