Related papers: Hard Lefschetz actions in Riemannian geometry with…
We study the problem of determining which diffeomorphism classes of K\"{a}hler manifolds admit a Hamiltonian circle action. Our main result is the following: Let $M$ be a closed symplectic manifold, diffeomorphic to a complete intersection…
Classification results are given for (i) compact quaternionic K\"ahler manifolds with a cohomogeneity-one action of a semi-simple group, (ii) certain complete hyperK\"ahler manifolds with a cohomogeneity-two action of a semi-simple group…
A compact symplectic manifold $(M, \omega)$ is said to satisfy the hard-Lefschetz condition if it is possible to develop an analogue of Hodge theory for $(M, \omega)$. This loosely means that there is a notion of harmonicity of differential…
We presented a systematic treatment of a Hilbert criterion for stability theory for an action of a real reductive group $G$ on a real submanifold $X$ of a K\"ahler manifold $Z$. More precisely, we suppose the action of a compact connected…
We study left-invariant pseudo-K\"ahler and hypersymplectic structures on semidirect products $G\rtimes H$; we work at the level of the Lie algebra $\mathfrak{g}\rtimes\mathfrak{h}$. In particular we consider the structures induced on…
Using methods originating in the theory of intersection spaces, specifically a de Rham type description of the real cohomology of these spaces by a complex of global differential forms, we show that the Leray-Serre spectral sequence with…
We prove the hard Lefschetz duality for locally conformally almost K\"{a}hler manifolds. This is a generalization of that for almost K\"{a}hler manifolds studied by Cirici and Wilson. We generalize the K\"{a}hler identities to prove the…
We give the first numerical calculation of the spectrum of the Laplacian acting on bundle-valued forms on a Calabi-Yau three-fold. Specifically, we show how to compute the approximate eigenvalues and eigenmodes of the Dolbeault Laplacian…
Denote by $Sp(k,l)$ the quaternionic symplectic group of signature $(k,l)$. We study the deformation rigidity of the embedding $Sp(k,l) \times Sp(1) \hookrightarrow H$, where $H$ is either $Sp(k+1,l)$ or $Sp(k,l+1)$, this is done by…
It is shown that any compact K\"ahler manifold $M$ gives canonically rise to two strongly homotopy algebras, the first one being associated with the Hodge theory of the de Rham complex and the second one with the Hodge theory of the…
Following a strictly geometric approach we construct globally supersymmetric scalar field theories on the supersphere, defined as the quotient space $S^{2|2} = UOSp(1|2)/\mathcal{U}(1)$. We analyze the superspace geometry of the…
We show that every effective smooth action of a Lie group G on a manifold M is a diffeomorphism from G onto its image in Diff(M), where the image is equipped with the subset diffeology of the functional diffeology.
The Hard Lefschetz Property (HLP) is an important property which has been studied in several categories of the symplectic world. For Sasakian manifolds, this duality is satisfied by the basic cohomology (so, it is a transverse property),…
Recently, a metric construction for the Calabi-Yau 3-folds from a four-dimensional hyperkahler space by adding a complex line bundle was proposed. We extend the construction by adding a U(1) factor to the holomorphic (3,0)-form, and obtain…
In this paper, we study a class of heterotic Landau-Ginzburg models. We show that the action can be written as a sum of BRST-exact and non-exact terms. The non-exact terms involve the pullback of the complexified Kahler form to the…
Possible irreducible holonomy algebras $\g\subset\sp(2m,\Real)$ of odd Riemannian supermanifolds and irreducible subalgebras $\g\subset\gl(n,\Real)$ with non-trivial first skew-symmetric prolongations are classified. An approach to the…
A suitable generalisation of the Lichnerowicz formula can relate the squares of supersymmetric operators to the effective action, the Bianchi identities for fluxes, and some equations of motion. Recently, such formulae have also been shown…
A geometrisation scheme internal to the category of Lie supergroups is discussed for the supersymmetric de Rham cocycles on the super-Minkowski group $\,\mathbb{T}\,$ which determine the standard super-$p$-brane dynamics with that target,…
Given a simple Lie group G of rank 1, we consider compact pseudo-Riemannian manifolds (M,g) of signature (p,q) on which G can act conformally. Precisely, we determine the smallest possible value for the index min(p,q) of the metric. When…
In this paper, we generalize all the results obtained on para-K\"ahler Lie algebras in Journal of Algebra {\bf 436} (2015) 61-101 to para-K\"ahler Lie algebroids. In particular, we study exact para-K\"ahler Lie algebroids as a…