arXiv research

Study of rational Picard group in moduli space of holomorphic n-differentials.

We introduce the concept of $N$-differential graded algebras (N-dga), and study the moduli space of deformations of the differential of a N-dga. We prove that it is controlled by what we call the N-Maurer-Cartan equation.

We construct geometric examples of N-differential graded algebras such as the algebra of differential forms of depth $N$ on an affine manifold, and $N$-flat covariant derivatives.

Local index theorem for cofinite hyperbolic Riemann surfaces derived from computational perspective.

The paper details local forms of morphisms in colored supermanifolds.

Study flat metrics from right prisms, finding non-lattice surfaces with translation coverings.

In this paper, we develop holomorphic Jacobi structures. Holomorphic Jacobi manifolds are in one-to-one correspondence with certain homogeneous holomorphic Poisson manifolds. Furthermore, holomorphic Poisson manifolds can be looked at as special cases of holomorphic Jacobi manifolds. We show that holomorphic Jacobi str…

Develops theory of d-holomorphic connections on Klein surfaces.

Survey on holomorphic structures on complex manifolds.

The goal of this paper is to study the theory of last multipliers in the framework of complex manifolds with a fixed holomorphic volume form. The motivation of our study is based on the equivalence between a holomorphic ODE system and an associated real ODE system and we are interested how we can relate holomorphic las…

Holomorphic Lie algebroid connections on Riemann surfaces are characterized.

Holomorphic Jacobi manifolds integrate to complex contact groupoids.

Classifies Kähler metrics with constant holomorphic curvature.

We introduce holomorphic Riemannian maps between almost Hermitian manifolds as a generalization of holomorphic submanifolds and holomorphic submersions, give examples and obtain a geometric characterization of harmonic holomorphic Riemannian maps from almost Hermitian manifolds to Kaehler manifolds.

New proof shows holomorphic sectional curvature fully determines curvature tensor.

Formula derived for holomorphic Poisson blow-ups.

Study on holomorphic isometries between complex domains, revealing geometric properties.

Flat holomorphic connections on stable bundles over LVMB manifolds are always flat.

The paper extends holomorphic motions over non-simply connected Riemann surfaces.

Study finds conditions for minimum of Donaldson's functional on Higgs bundles with non-holomorphic Higgs fields.

Introduces quasi-holomorphic maps and their properties.

We study holomorphic Poisson manifolds and holomorphic Lie algebroids from the viewpoint of real Poisson geometry. We give a characterization of holomorphic Poisson structures in terms of the Poisson Nijenhuis structures of Magri-Morosi and describe a double complex which computes the holomorphic Poisson cohomology. A …

Holomorphic cylinders converge to disks joined by flow lines.

Holomorphic discs cover a ball in complex space.

Deformation theory for holomorphic Cartan geometries studied.

Extends holomorphic Cartan geometry to Sasakian manifolds.

Holomorphic structures on Oeljeklaus-Toma manifolds are shown to be locally homogeneous.

Paper describes holomorphic polyvector fields on toric varieties.

Study connections on complex Riemann surfaces for Lie algebroid structures.

The study classifies holomorphic projective connections on complex threefolds.

Study on complex tori foliations and flat geometries.

Introduces new holomorphic contact structures and proves unobstructedness theorems.

Every holomorphic effective parabolic or reductive geometry on a domain over a Stein manifold extends uniquely to the envelope of holomorphy of the domain. This result completes the open problems of my earlier paper on extension of holomorphic geometric structures on complex manifolds. We use this result to classify th…

In this paper, we find a holomorphic Darboux chart around any immersed noncompact holomorphic Legendrian curve in a complex contact manifold $(X,ξ)$. By using such a chart, we show that every holomorphic Legendrian immersion $R\to X$ from an open Riemann surface can be approximated on relatively compact subsets by holo…

We introduce a natural generalisation of holomorphic curves to morphisms of supermanifolds, referred to as holomorphic supercurves. More precisely, supercurves are morphisms from a Riemann surface, endowed with the structure of a supermanifold which is induced by a holomorphic line bundle, to an ordinary almost complex…

Holomorphic metrics on complex manifolds imply infinite fundamental groups.

Study anti-invariant submersions from holomorphic statistical manifolds.

Classifies holomorphic parabolic geometries on complex manifolds.

Study holomorphic isometric embeddings between symmetric domains, focusing on total geodesy.

Study compact Kähler manifolds with nonpositive holomorphic sectional curvature and their canonical bundles.

Construct Kähler metrics with negative holomorphic bisectional curvature on compact relative Kähler fibrations.

Study holomorphic sections of Deligne-Hitchin space, answering Simpson's question.

Study on holomorphic discs in bundles over compact surfaces, proving Fredholm regularity under certain conditions.

Study optimal holomorphic extensions for jets along submanifolds as tensor powers increase.

Extends residue theory to flags of holomorphic distributions.

The classical Hadamard three circle theorem is generalized to complete Kähler manifolds. More precisely, we show that the nonnegativity of the holomorphic sectional curvature is a necessary and sufficient condition for the three circle theorem. As corollaries, two sharp monotonicity formulae for holomorphic functions a…

In this paper, we study deformations of holomorphic Poisson maps which extend Horikawa's series of papers on deformations of holomorphic maps in the context of holomorphic Poisson deformations. In appendices, we present deformations of Poisson morphisms in the language of functors of Artin rings which is the algebraic …

The Fubini-Study metric minimizes a volume-normalized holomorphic systole in $\mathbb{C}P^n$.