Related papers: Quaternionic Kahler Manifolds, Constrained Instant…

Various curvature conditions are studied on metrics admitting a symmetry group. We begin by examining a method of diagonalizing cohomogeneity-one Einstein manifolds and determine when this method can and cannot be used. Examples, including…

We discuss instantons on noncommutative four-dimensional Euclidean space. In commutative case one can consider instantons directly on Euclidean space, then we should restrict ourselves to the gauge fields that are gauge equivalent to the…

We consider Fano manifolds M that admit a collection of finite automorphism groups G_1, ..., G_k, such that the quotients M/G_i are smooth Fano manifolds possessing a Kaehler-Einstein metric. Under some numerical and smoothness assumptions…

We present an explicit upper bound on the number of isolated homogeneous Einstein metrics on compact homogeneous spaces whose isotropy representations consist of pairwise inequivalent irreducibles. This is the BKK bound of the corresponding…

We study instanton and Ulrich bundles on hypersurfaces of the projective space, with a focus on special cubic fourfolds and generalized Pfaffians, notably defined by skew-symmetric endomorphisms of Steiner bundles. We prove that the acyclic…

Let (M,h) be a compact 4-dimensional Einstein manifold, and suppose that h is Hermitian with respect to some complex structure J on M. Then either (M,J,h) is Kaehler-Einstein, or else, up to rescaling and isometry, it is one of the…

The goal of this book is to characterize algebraically the closed 4-manifolds that fibre nontrivially or admit geometries in the sense of Thurston, or which are obtained by surgery on 2-knots, and to provide a reference for the topology of…

We investigate membrane and fivebrane instanton effects in type IIA string theory compactified on rigid Calabi-Yau manifolds. These effects contribute to the low-energy effective action of the universal hypermultiplet, in four dimensional…

We study the interaction between toric Ricci-flat metrics in dimension 4 and axisymmetric harmonic maps from the 3-dimensional Euclidean space into the hyperbolic plane. Applications include (1). The construction of complete Ricci-flat…

We construct the Einstein equation for an invariant Riemannian metric on the exceptional full flag manifold $M=G_2/T$. By computing a Gr\"obner basis for a system of polynomials of multi-variables we prove that this manifold admits exactly…

Supersymmetric domain-wall spacetimes that lift to Ricci-flat solutions of M-theory admit generalized Heisenberg (2-step nilpotent) isometry groups. These metrics may be obtained from known cohomogeneity one metrics of special holonomy by…

We apply the methods recently developed for computation of type IIA disk instantons using mirror symmetry to a large class of D-branes wrapped over Lagrangian cycles of non-compact Calabi-Yau 3-folds. Along the way we clarify the notion of…

We present a unified eight-dimensional approach to instanton equations on several seven-dimensional manifolds associated to a six-dimensional homogeneous nearly K\"ahler manifold. The cone over the sine-cone on a nearly K\"ahler manifold…

In this paper, we investigate the nature of Einstein solitons, whether it is steady, shrinking or expanding on almost $\alpha$-cosymplectic $3$-manifolds. We also prove that a simply connected homogeneous almost $\alpha$-cosymplectic…

We show that every quaternion-K\"ahler manifold of negative scalar curvature is stable as an Einstein manifold and therefore scalar curvature rigid. In particular, this implies that every irreducible nonpositive Einstein manifold of special…

We search for an abelian description of the Yang-Mills instantons on certain eight dimensional manifolds with the special holonomies $Spin(7)$ and SU(4). By mimicing the Seiberg-Witten theory in four dimensions, we propose a set of…

We show that the resolution of moduli space of ideal instantons parameterizes the instantons on non-commutative $\IR^{4}$. This moduli space appears as a Higgs branch of the theory of $k$ $D0$-branes bound to $N$ $D4$-branes by the…

Let $M$ be a pseudo-Riemannian spin manifold of dimension $n$ and signature $s$ and denote by $N$ the rank of the real spinor bundle. We prove that $M$ is locally homogeneous if it admits more than ${3/4}N$ independent Killing spinors with…

We consider a general 4n-dimensional quaternionic Kahler geometry with a free action of the torus T^(n+1). The toric action lifts onto the Swann bundle of the quaternionic Kahler space to a tri-holomorphic action that commutes with the…

In this paper, we study the solvmanifolds constructed from any parabolic subalgebras of any semisimple Lie algebras. These solvmanifolds are naturally homogeneous submanifolds of symmetric spaces of noncompact type. We show that the Ricci…