arXiv research

New framework mated Kleinian groups with complex polynomials, revealing unique group properties.

Unified and generalized mating frameworks for Kleinian groups and rational maps.

Study natural and conjugate mates of Frenet curves in Lie groups.

New method proves mateability of triangle groups with Blaschke products.

This note gives sufficient conditions (isothermic or totally nonisothermic) for an immersion of a compact surface to have no Bonnet mate.

Study of holomorphic correspondences combining entire maps and Fuchsian groups.

The paper connects reflection groups to maps with specific dynamical properties.

In this work, we studied the properties of the spherical indicatrices of a Bertrand curve and its mate curve and presented some characteristic properties in the cases that Bertrand curve and its mate curve are slant helices, spherical indicatrices are slant helices and we also researched that whether the spherical indi…

We present a novel method for solving Canonical Correlation Analysis (CCA) in a sparse convex framework using a least squares approach. The presented method focuses on the scenario when one is interested in (or limited to) a primal representation for the first view while having a dual representation for the second view…

The Bonnet problem is solved for specific Thurston geometries.

The paper studies degenerations of rational maps and their limits as geometrically finite rational maps.

Automated model tracks mouse behavior in home cages.

The study of Bonnet surfaces in 4D space forms reveals new conformally invariant properties and characterizes proper Bonnet surfaces.

Overview of dynamics in algebraic correspondences and their connections.

In this work, we study plane and spherical curves in Euclidean and Lorentz-Minkowski 3-spaces by employing rotation minimizing (RM) frames. By conveniently writing the curvature and torsion for a curve on a sphere, we show how to find the angle between the principal normal and an RM vector field for spherical curves. L…

With recent advances in high throughput technology, researchers often find themselves running a large number of hypothesis tests (thousands+) and esti- mating a large number of effect-sizes. Generally there is particular interest in those effects estimated to be most extreme. Unfortunately naive estimates of these effe…

Single-cell RNA sequencing (scRNA-seq) is a fast growing approach to measure the genome-wide transcriptome of many individual cells in parallel, but results in noisy data with many dropout events. Existing methods to learn molecular signatures from bulk transcriptomic data may therefore not be adapted to scRNA-seq data…

Survey explores interactions between four conformal dynamics branches.

In this article, we introduce rack invariants of oriented Legendrian knots in the 3-dimensional Euclidean space endowed with the standard contact structure, which we call Legendrian racks. These invariants form a generalization of the quandle invariants of knots. These rack invariants do not result in a complete invari…

Optimizing a neural network's performance is a tedious and time taking process, this iterative process does not have any defined solution which can work for all the problems. Optimization can be roughly categorized into - Architecture and Hyperparameter optimization. Many algorithms have been devised to address this pr…

Develops analogs of character varieties for algebraic correspondences, proving boundedness and compactifications.

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.

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.

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

This is the second part of a series of two papers dedicated to a systematic study of holomorphic Jacobi structures. In the first part, we introduced and study the concept of a holomorphic Jacobi manifold in a very natural way as well as various tools. In the present paper, we solve the integration problem for holomorph…

Introduces quasi-holomorphic maps and their properties.

Holomorphic cylinders converge to disks joined by flow lines.

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

Paper describes holomorphic polyvector fields on toric varieties.

Let $E$ be a closed set in the Riemann sphere $\widehat{\mathbb{C}}$. We consider a holomorphic motion $φ$ of $E$ over a complex manifold $M$, that is, a holomorphic family of injections on $E$ parametrized by $M$. It is known that if $M$ is the unit disk $Δ$ in the complex plane, then any holomorphic motion of $E$ ove…

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…

Study anti-invariant submersions from holomorphic statistical manifolds.

Classifies holomorphic parabolic geometries on complex manifolds.