Related papers: Infinitesimal Variation of Harmonic Forms and Lefs…

We introduce the notion of infinitesimal variations of mixed Hodge structures and invariants associated to them. We describe these invariants in the case of a pair $(X,Y)$ with $X$ a Fano 3-fold and $Y$ a smooth anticanonical K3 surface and…

It is developed the theory of the Dirichlet problem for harmonic functions. On this basis, for the nondegenerate Beltrami equations in the quasidisks and, in particular, in the smooth domains, it is proved the existence of regular solutions…

We consider a manifestly Lorentz invariant form $\mathbb L$ of the biquaternion algebra and its generalization to the case of curved manifold. The conditions of $\mathbb L$-differentiability of $\mathbb L$-functions are formulated and…

In this paper, we will analyse a supersymmetric field theory deformed by generalized uncertainty principle and Lifshitz scaling. It will be observed that this deformed supersymmetric field theory contains non-local fractional derivative…

Compact K\"{a}hler manifolds satisfy several nice Hodge-theoretic properties such as the Hodge symmetry, the Hard Lefschetz property and the Hodge-Riemann bilinear relations, etc. In this note, we investigate when such nice properties hold…

We study the infinitesimal variation of Hodge structure associated with families of reduced algebraic curves with singularities. The analysis applies to curves beyond the nodal case and is not restricted to plane curves, encompassing curves…

We study the concept of (generalized) $p$-th variation of a real-valued continuous function along a general class of refining sequence of partitions. We show that the finiteness of the $p$-th variation of a given function is closely related…

In an earlier paper, we showed that the moduli space of deformations of a smooth, compact, orientable special Lagrangian submanifold L in a symplectic manifold X with a non-integrable almost complex structure is a smooth manifold of…

We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively. We also explore their certain difference…

Associated varieties are geometric objects appearing in infinite-dimensional representations of semisimple Lie algebras (groups). By applying Fourier transformations to the natural orthogonal oscillator representations of special linear Lie…

Equivariant localization expresses global invariants in terms of local invariants, and many of them appearing in equivariant index theory, (holomorphic) Morse theory, geometric quantization and supersymmetric localization can be…

Let Y be a compact reduced subspace of a complex manifold X, and let F be a subsheaf of the tangent bundle T_X which is closed under the Lie bracket. This paper discusses criteria to guarantee that infinitesimal deformations of the…

We construct real polarizable Hodge structures on the reduced leafwise cohomology of K\"ahler-Riemann foliations by complex manifolds. As in the classical case one obtains a hard Lefschetz theorem for this cohomology. Serre's K\"ahlerian…

For a field of characteristic $\ne 2$ we study vector spaces that are graded by the weight lattice of a root system, and are endowed with linear operators in each simple root direction. We show that these data extend to a graded semisimple…

Pseudo-harmonic morphisms give rise on the domain space to a distribution which admits an almost complex structure compatible with the given Riemannian metric. We shall show that this property, together with the harmonicity, are preserved…

The Lichnerowicz conjecture asserts that all harmonic manifolds are either flat or locally symmetric spaces of rank 1. This conjecture has been proved by Z.I. Szabo for harmonic manifolds with compact universal cover. E. Damek and F. Ricci…

A setting for global variational geometry on Grassmann fibrations is presented. The integral variational functionals for finite dimensional immersed submanifolds are studied by means of the fundamental Lepage equivalent of a homogeneous…

We prove that the irreducible components of the space of framed deformations of a $2$-dimensional mod $2$ representation with scalar semi-simplification of the absolute Galois group of $\mathbb{Q}_2$ are in natural bijection with those of…

We study the Witten--Reshetikhin--Turaev SU(2) invariant for the Seifert manifold $S^3/\Gamma$ where $\Gamma$ is a finite subgroup of SU(2). We show that the WRT invariants can be written in terms of the Eichler integral of the modular…

An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…