Related papers: Holomorphic vector fields and quadratic differenti…

We give a geometrical demonstration to the existence of holomorphic first integrals for certain kind of vector fields in $\mathbb{C}^2$ and $\mathbb{C}^3$.

We describe the space of measured foliations induced on a compact Riemann surface by meromorphic quadratic differentials. We prove that any such foliation is realized by a unique such differential $q$ if we prescribe, in addition, the…

Holomorphic modular bootstrap is an approach to classifying rational conformal field theories making use of the modular differential equations. In this paper we explore its flavored refinement. For a class of chiral algebras, we propose…

We consider a quadratic form defined on the surfaces with parallel mean curvature vector of an any dimensional complex space form and prove that its $(2,0)$-part is holomorphic. When the complex dimension of the ambient space is equal to…

Let $A$ be a commutative Banach algebra. Let $M$ be a complex manifold on $A$ (an $A$-manifold). Then, we define an $A$-holomorphic vector bundle $(\wedge^kT^*)(M)$ on $M$. For an open set $U$ of $M$, $\omega$ is said to be an…

We prove that a singular complex surface that admits a complete holomorphic vector field that has no invariant curve through a singular point of the surface is obtained from a Kato surface by contracting some divisor (in particular, it is…

For any twisted ideal polygon in $\mathbb{H}^3$, we construct a harmonic map from $\mathbb{C}$ to $\mathbb{H}^3$ with a polynomial Hopf differential, that is asymptotic to the given polygon, and is a bounded distance from a pleated plane.…

If a mapping of several complex variables into projective space is holomorphic in each pair of variables, then it is globally holomorphic.

We use the gradients of theta functions at odd two-torsion points --- thought of as vector-valued modular forms --- to construct holomorphic differential forms on the moduli space of principally polarized abelian varieties, and to…

In this paper we study differential forms and vector fields on the orbit space of a proper action of a Lie group on a smooth manifold, defining them as multilinear maps on the generators of infinitesimal diffeomorphisms, respectively. This…

We characterize harmonic spaces in terms of the dimensions of various spaces of radial eigen-spaces of the Laplacian $\Delta^0$ on functions and the Laplacian $\Delta^1$ on 1-forms. We examine the nature of the singularity as the geodesic…

We classify holomorphic Cartan geometries on every compact complex curve, and on every compact complex surface which contains a rational curve.

Nonholonomic systems are variational models commonly used for mechanical systems with ideal no-slip constraints. This note provides a differential-geometric derivation of the nonholonomic equations of motion for an arbitrary rigid body…

A meromorphic quadratic differential with poles of order two, on a compact Riemann surface, induces a measured foliation on the surface, with a spiralling structure at any pole that is determined by the complex residue of the differential…

An odd vector field $Q$ on a supermanifold $M$ is called homological, if $Q^2=0$. The operator of Lie derivative $L_Q$ makes the algebra of smooth tensor fields on $M$ into a differential tensor algebra. In this paper, we give a complete…

Every oriented 4-manifold admits a folded symplectic structure, which in turn determines a homotopy class of compatible almost complex structures that are discontinuous across the folding hypersurface ("fold") in a controlled fashion. We…

For T $\Omega$ a Hermitian symmetric tube-type domain, a family ($\pi$ $\mu$) $\mu$$\in$C of holomorphic vector-valued representations is studied. The corresponding Wallach set is determined. The main tool is a realization of the…

The discrete Laplacian on Euclidean triangulated surfaces is a well-established notion. We introduce discrete Laplacians on spherical and hyperbolic triangulated surfaces. On the one hand, our definitions are close to the Euclidean one in…

We prove a theorem which asserts that the Lie algebra of all holomorphic vector fields on a compact K\"ahler manifold with a perturbed extremal metric has the structure similar to the case of an unperturbed extremal K\"ahler metric proved…

Let $(\Sigma,p)$ be a pointed Riemann surface of genus $g\geq 1$. For any integer $k\geq 1$, we parametrize the space of meromorphic quadratic differentials on $\Sigma$ with a pole of order $(k+2)$ at $p$, having a connected critical graph…