Related papers: Hyperkahler implosion and Nahm's equations

In this paper we study the homogeneous Kaehler manifolds (h.K.m.) which can be Kaehler immersed into finite or infinite dimensional complex space forms. On one hand we completely classify the h.K.m. which can be Kaehler immersed into a…

In this paper, we study supersymmetric or bi-superhamiltonian Euler equations related to the generalized Neveu-Schwarz algebra. As an application, we obtain several supersymmetric or bi-superhamiltonian generalizations of some well-known…

We develop a Helmholtz-like theorem for differential forms in Euclidean space $E_{n}$ using a uniqueness theorem similar to the one for vector fields. We then apply it to Riemannian manifolds, $R_{n}$, which, by virtue of the…

We discuss orientifold projections on superspace effective actions for hypermultiplets. We present a simple and new mechanism that allows one to find the Kahler potential and complex structure for the N=1 theory directly in terms of the…

In this article, we will explore the fundamental concepts, including various basic concepts on $d$-complex manifolds, along with several differential operators and examine the relationships between them. A $d$-K\"ahler manifold is a…

Hom-Lie algebras are generalizations of Lie algebras that arise naturally in the study of nonassociative algebraic structures. In this paper, the concepts of solvable and nilpotent Hom-Lie algebras studied further. In the theory of groups,…

We show that Hardy's uncertainty principle can be reformulated in such a way that it has an analogue even for compact Lie groups and symmetric spaces of compact type.

Starting with the projective-superspace off-shell formulation for four-dimensional N = 2 supersymmetric sigma-models on cotangent bundles of arbitrary Hermitian symmetric spaces, their on-shell description in terms of N = 1 chiral…

We consider integrable Hamiltonian systems in a general setting of invariant submanifolds which need not be compact. For instance, this is the case a global Kepler system, non-autonomous integrable Hamiltonian systems and integrable systems…

Let (M,I) be a compact Kaehler manifold admitting a hypercomplex structure. We show that (M, I) admits a natural HKT-metric. This is used to construct a holomorphic symplectic form on (M,I).

This paper is a discussion of relations between some free-boundary problems and infinite dimensional Lie groups; particularly a version of Nahm's equations for the group of Hamiltonian diffeomorphisms in two dimensions.

We give a formula for the radial asymptotics to all orders of the special $q$-hypergeometric series known as Nahm sums at complex roots of unity. This result is used in~\cite{CGZ} to prove one direction of Nahm's conjecture relating the…

We study universal enveloping Hopf algebras of Lie algebras in the category of weakly complete vector spaces over the real and complex field.

We prove estimates for the sectional curvature of hyperkaehler quotients and give applications to moduli spaces of solutions to Nahm's equations and Hitchin's equations.

In this paper, we investigate the compactness of nonnegative solutions to a critical sub-elliptic equation with a nonnegative potential on the Heisenberg group. We establish that the solution set is compact provided the potential satisfies…

We prove several results on the structure of solvable quotients of fundamental groups of compact Kahler manifolds (Kahler groups).

Let X be a compact Kaehler manifold. We expect that any direct sum decomposition of the tangent bundle T(X) comes from a splitting of the universal covering space of X as a product of manifolds, in such a way that the given decomposition of…

In this paper we apply the hyper-K\"ahler quotient construction to Lie groups with a left invariant hyper-K\"ahler structure under the action of a closed abelian subgroup by left multiplication. This is motivated by the fact that some known…

We present an explicit integration formula for the Haar integral on a compact connected Lie group. This formula relies on a known decomposition of a compact connected simple Lie group into symplectic leaves, when one views the group as a…

Suppose that M is a complete hyperkahler manifold with a compact Lie group K acting via hyperkahler isometries and with hyperkahler moment map $(\mu_{\mathbb{C}}, \mu_{\mathbb{R}}): M\rightarrow…