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.

We find complete expanding Kähler-Ricci solitons of two types. The first are cohomogeneity one under the action (2m - 1)-dimensional Heisenberg group or a certain quotient it, for any m ? 2. second type, which generalizes first, reside on ?*-bundles over compact Kähler Ricci-flat manifolds, admit an S1 by isometries, and have ends. Both types local structure stemming from ansatz described in [2...

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 classify, up to orbit equivalence, all cohomogeneity one actions on the hyperbolic planes over the complex, quaternionic and Cayley numbers, and on the complex hyperbolic spaces CH, n ≥ 3. For the quaternionic hyperbolic spaces HH, n ≥ 3, we reduce the classification problem to a problem in quaternionic linear algebra and obtain partial results. For real hyperbolic spaces, this classificatio...

We examine the thermodynamics of Euclidean dyonic Taub-NUT/Bolt-AdS4 black holes for a variety horizon geometries to understand how gauge field regularity conditions influence thermodynamic relations. find several distinct features that distinguish NUT-charged case from its Reissner-Nordstrom counterpart. For NUT solution, vanishes at and so is ensured. Bolt solution we norm required vanish in ...

Special Lagrangian submanifolds of complex Euclidean space C have been studied widely over the last few years. These submanifolds are volume minimizing and, in particular, they are minimal submanifolds. When n = 2, special Lagrangian surfaces of C are exactly complex surfaces with respect to another orthogonal complex structure on R ≡ C. A very important problem here, and even a good starting p...

We show that noncompact homogeneous spaces not diffeomorphic to Euclidean space of dimension 9 or 10 admit no Einstein metrics negative Ricci curvature, with only three potential exceptions. The main ingredient in the proof is show, via a cohomogeneity-one approach, admitting an ideal isomorphic $ \mathfrak{sl}_2(\mathbb{R}) curvature.

We construct all possible complete metrics of cohomogeneity one G2 holonomy with S × S principal orbits from gauged supergravity. Our approach rests on a generalization of the twisting procedure used in this framework. It corresponds to a non-trivial embedding of the special Lagrangian three–cycle wrapped by the D6–branes in the lower dimensional supergravity. There are constraints that neatly ...