Related papers: $G_2$-Holonomy Metrics Connected with a 3-Sasakian…

We construct a new (singular) cohomogeneity-three metric of G_2 holonomy. The solution can be viewed as a triple intersection of smeared Taub-NUTs. The metric comprises three non-compact radial-type coordinates, with the principal orbits…

We consider spaces M_7 and M_8 of G_2 holonomy and Spin(7) holonomy in seven and eight dimensions, with a U(1) isometry. For metrics where the length of the associated circle is everywhere finite and non-zero, one can perform a Kaluza-Klein…

We decompose linear $\mathrm{G}_2$-structure in canonical ways adapted to 3-dimensional subspaces, in terms of certain natural 1-forms and definite triple of 2-forms, and apply the decompositions to the study of $\mathrm{G}_2$-structure…

A Hermitian metric $\omega$ on a complex manifold is called SKT or pluriclosed if $dd^c\omega=0$. Let M be a twistor space of a compact, anti-selfdual Riemannian manifold, admitting a pluriclosed Hermitian metric. We prove that in this case…

We consider invariant Riemannian metrics on compact homogeneous spaces $G/H$ where an intermediate subgroup $K$ between $G$ and $H$ exists. In this case, the homogeneous space $G/H$ is the total space of a Riemannian submersion. The metrics…

A $\mathbb Z_2$-harmonic spinor on a 3-manifold $Y$ is a solution of the Dirac equation on a bundle that is twisted around a submanifold $\mathcal Z$ of codimension 2 called the singular set. This article investigates the local structure of…

Geodesic orbit spaces (or g.o. spaces) are defined as those homogeneous Riemannian spaces $(M=G/H,g)$ whose geodesics are orbits of one-parameter subgroups of $G$. The corresponding metric $g$ is called a geodesic orbit metric. We study the…

A GL(2, R) structure on an (n+1)-dimensional manifold is a smooth pointwise identification of tangent vectors with polynomials in two variables homogeneous of degree n. This, for even n=2k, defines a conformal structure of signature (k,…

We study the moduli space of $G_2$-instantons on (projectively) flat bundles over torsion-free $G_2$-orbifolds. We prove that the moduli space is compact and smooth at the irreducible locus after adding small and generic holonomy…

There is a rich theory of so-called (strict) nearly Kaehler manifolds, almost-Hermitian manifolds generalising the famous almost complex structure on the 6-sphere induced by octonionic multiplication. Nearly Kaehler 6-manifolds play a…

We study collections of exact Lagrangian submanifolds respecting some uniform Riemannian bounds, which we equip with a metric naturally arising in symplectic topology (e.g. the Lagrangian Hofer metric or the spectral metric). We exhibit…

We propose new $G_2$-holonomy manifolds, which geometrize the Gaiotto-Kim 4d N=1 duality domain walls of 5d N=1 theories. These domain walls interpolate between different extended Coulomb branch phases of a given 5d superconformal field…

We classify 7-dimensional cocalibrated $\G_2$-manifolds with parallel characteristic torsion and non-abelian holonomy. All these spaces admit a metric connection $\nabla^{\mathrm{c}}$ with totally skew-symmetric torsion and a spinor field…

We construct new examples of non-formal simply connected compact Sasaki-Einstein 7-manifolds. We determine the minimal model of the total space of any fibre bundle over $CP^2$ with fibre $S^1\times S^2$ or $S^3/Z_p$ ($p>0$), and we apply…

We discuss some geometric aspects of PSL(2,C), SL(2,C), and the space G of the geodesics of H^3 equipped with some suitable structures of Riemannian holomorphic manifolds of constant sectional curvature. We also observe that G is a…

We give a full geometrical description of local totally geodesic unit vector field on Riemannian 2-manifold, considering the field as a local imbedding of the manifold into its unit tangent bundle with the Sasaki metric.

We give an answer to a question posed recently by R.Bryant, namely we show that a compact 7-dimensional manifold equipped with a G2-structure with closed fundamental form is Einstein if and only if the Riemannian holonomy of the induced…

In this article, we consider $L^{2}$ harmonic forms on a complete non-compact Riemannian manifold $X$ with a nonzero parallel form $\omega$. The main result is that if $(X,\omega)$ is a complete $G_{2}$- ( or $Spin(7)$-) manifold with a…

On a closed connected oriented manifold $M$ we study the space $\mathcal{M}_\|(M)$ of all Riemannian metrics which admit a non-zero parallel spinor on the universal covering. Such metrics are Ricci-flat, and all known Ricci-flat metrics are…

We give a description of all $G$-invariant Ricci-flat K\"ahler metrics on the canonical complexification of any compact Riemannian symmetric space $G/K$ of arbitrary rank, by using some special local $(1,0)$ vector fields on $T(G/K)$. As…