Related papers: K\"{a}hler Solitons, Contact Structures, and Isopa…
We introduce the notions of $\mathbb{K}$-framings, based $\mathbb{K}$-framings and relative $\mathbb{K}$-framings of a compact connected oriented surface $\Sigma$ for any commutative ring $\mathbb{K}$ with unit, and a map which maps a based…
We investigate the robustness of some recent results obtained for homogeneous and isotropic cosmological models with conformally coupled scalar fields. For this purpose, we investigate anisotropic homogeneous solutions of the models…
We classify complete curvature homogeneous metrics on simply connected four dimensional manifolds which are invariant under a cohomogeneity one action. We show that they are either isometric to a symmetric space with one of its…
We study a Boltzmann's type entropy functional (which appeared in existing literature) defined on K\"ahler metrics of a fixed K\"ahler class. The critical points of this functional are gradient K\"ahler-Ricci solitons, and the functional…
We obtain a structure theorem for the group of holomorphic automorphisms of a conformally K\"ahler, Einstein-Maxwell metric, extending the classical results of Matsushima, Licherowicz and Calabi in the K\"ahler-Einstein, cscK, and extremal…
We observe that the class of metric $f$-$K$-contact manifolds, which naturally contains that of $K$-contact manifolds, is closed under forming mapping tori of automorphisms of the structure. We show that the de Rham cohomology of compact…
We report a new class of $SO(3,\mathbb{C})$ and diffeomorphism invariant formulations for general relativity with either a vanishing or a nonvanishing cosmological constant, which depends functionally on a $SO(3,\mathbb{C})$ gauge…
A powerful tool for studying the behavior of classical field theories is Derrick's theorem: one may rule out the existence of localized inhomogeneous stable field configurations (solitons) by inspecting the Hamiltonian and making scaling…
Let $G$ denote an infinite-dimensional Heisenberg-like group, which is a class of infinite-dimensional step 2 stratified Lie groups. We consider holomorphic functions on $G$ that are square integrable with respect to a heat kernel measure…
In this paper we define a new cohomology of a smooth manifold called Lichnerowicz type cohomology attached to a function. Firstly, we study some basic properties of this cohomology as: a de Rham type isomorphism, dependence on the function,…
We derive the geodesic equation for relatively K\"ahler metrics on fibrations and prove that any two such metrics with fibrewise constant scalar curvature are joined by a unique smooth geodesic. We then show convexity of the log-norm…
We review the emergence of hypergeometric structures (of $F_4$ Appell functions) from the conformal Ward identities (CWIs) in conformal field theories (CFTs) in dimensions $d > 2$. We illustrate the case of scalar 3- and 4-point functions.…
A classical result of D. McDuff asserts that a simply-connected complete Kaehler manifold $(M,g,\omega)$ with non positive sectional curvature admits global symplectic coordinates through a symplectomorphism $\Psi: M\rightarrow R^{2n}$…
On a (pseudo-)Riemannian manifold (MM,g), some fields of endomorphisms i.e. sections of End(TMM) may be parallel for g. They form an associative algebra A, which is also the commutant of the holonomy group of g. As any associative algebra,…
We consider the Seiberg-Witten solution of pure $\mathcal{N} =2$ gauge theory in four dimensions, with gauge group $SU(N)$. A simple exact series expansion for the dependence of the $2 (N-1)$ Seiberg-Witten periods $a_I(u), a_{DI}(u)$ on…
The target space of a (4,0) supersymmetric two-dimensional sigma model with Wess-Zumino term has a connection with totally skew-symmetric torsion and holonomy contained in Sp(n).Sp(1), QKT-connection. We study the geometry of…
In this paper, we apply the geometric Hamilton--Jacobi theory to obtain solutions of classical hamiltonian systems that are either compatible with a cosymplectic or a contact structure. As it is well known, the first structure plays a…
In the dimer model, a configuration consists of a perfect matching of a fixed graph. If the underlying graph is planar and bipartite, such a configuration is associated to a height function. For appropriate "critical" (weighted) graphs,…
Let $L_f$ be a link of an isolated hypersurface singularity defined by a weighted homogenous polynomial $f.$ In this article, we give ten examples of $2$-connected seven dimensional Sasaki-Einstein manifolds $L_f$ for which $H_{3}(L_f,…
Curvature properties of a metric connection with totally skew-symmetric torsion are investigated. It is shown that if either the 3-form $T$ is harmonic, $dT=\delta T=0$ or the curvature of the torsion connection $R\in S^2\Lambda^2$ then the…