Related papers: Special Hermitian metrics and Lie groups

We find that the target space of two-dimensional (4,0) supersymmetric sigma models with torsion coupled to (4,0) supergravity is a QKT manifold, that is, a quaternionic K\"ahler manifold with torsion. We give four examples of geodesically…

Answering a conjecture by S. Kobayashi, in 1986, K. Sekigawa and L. Vanhecke proved that an almost hermitian manifold whose local geodesic symmetries preserve the K\"ahler 2-form is a locally symmetric hermitian space. In the present paper,…

In the present paper we study SKT and generalized K\"ahler structures on solvable Lie algebras with (not necessarily abelian) codimension two nilradical. We treat separately the case of $J$-invariant nilradical and non $J$-invariant…

In this paper, we give a new method to construct a compact symplectic manifold which does not satisfy the hard Lefschetz property. Using our method, we construct a simply connected compact K\"ahler manifold $(M,J,\omega)$ and a symplectic…

Connections with (skew-symmetric) torsion on non-symmetric Riemannian manifold satisfying the Einstein metricity condition (NGT with torsion) are considered. It is shown that an almost Hermitian manifold is an NGT with torsion if and only…

We study Riemannian manifolds carrying a metric connection with parallel, skew-symmetric and closed torsion, which we call in short PSCT manifolds. We prove that PSCT manifolds always locally split into a product of well-understood factors,…

We construct symplectic structures on roughly half of all equal rank biquotients of the form $G//T$, where $G$ is a compact simple Lie group and $T$ a torus, and investigate Hamiltonian Lie group actions on them. For the Eschenburg flag,…

We define $(p,q)$ hermitian geometry as the target space geometry of the two dimensional $(p,q)$ supersymmetric sigma model. This includes generalised K\"{a}hler geometry for $(2,2)$, generalised hyperk\"{a}hler geometry for $(4,2)$, strong…

We compute the first two symplectic quadratic K-theory groups of the integers, or equivalently, the first two stable homology groups of the group of symplectic integral matrices preserving the standard quadratic refinement. The main novelty…

We give a new method for calculation of complex and biHermitian structures on low dimensional real Lie algebras. In this method, using non-coordinate basis, we first transform the Nijenhuis tensor field and biHermitian structure relations…

Having fixed a Kaehler class and the unique corresponding hyperkaehler metric, we prove that all special Lagrangian submanifolds of an irreducible symplectic 4-fold X are bi-Lagrangian and that they are obtained by complex submanifolds via…

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 show that complex Lie algebras (in particular sl(2,C)) provide us with an elegant method for studying the transition from real to complex eigenvalues of a class of non-Hermitian Hamiltonians: complexified Scarf II, generalized…

An old open question in non-K\"ahler geometry predicts that any compact Hermitian manifold with constant holomorphic sectional curvature must be K\"ahler or Chern flat. The conjecture is known to be true in dimension $2$ due to the work by…

We prove that any $4$-dimensional almost-K\"ahler Lie algebra of constant Hermitian holomorphic sectional curvature with respect to the canonical Hermitian connection is K\"ahler.

A $\mathrm{G}_2$-structure on a $7$-manifold $M$ is called a $\mathrm{G}_2T$-structure if $M$ admits a $\mathrm{G}_2$-connection $\nabla^T$ with totally skew-symmetric torsion $T_\varphi$. If furthermore, $T_\varphi$ is closed then it is…

We study symplectic structures on characteristically nilpotent Lie algebras (CNLAs) by computing the cohomology space $H^2(\Lg,k)$ for certain Lie algebras $\Lg$. Among these Lie algebras are filiform CNLAs of dimension $n\le 14$. It turns…

We consider homogeneous hypercomplex manifolds with a transitive action of a compact Lie group and we give a characterization of invariant HKT metrics on them. On every such hypercomplex manifold we prove the existence of an invariant…

We show that the existence of a left-invariant pluriclosed Hermitian metric on a unimodular Lie group with a left-invariant abelian complex structure forces the group to be $2$-step nilpotent. Moreover, we prove that the pluriclosed flow…

This is the first of two papers devoted to showing how the rich algebraic formalism of Eliashberg-Givental-Hofer's symplectic field theory (SFT) can be used to define higher algebraic structures on the symplectic cohomology of open…