arXiv research

Calabi-Yau theorem extended to Vaisman manifolds.

New theorem on Lee classes for LCK manifolds with potential.

This note is devoted to partial study of recurrent equation $dω=β\wedge ω$, based on linear algebra of exterior forms. Such equation was considered by Lee, for non-degenerate 2-form. In this note we approach general case, when $ω$ is arbitrary. Particularly, we extend results obtained by Lee, on odd-forms.

Study examines Weyl structures on Riemannian manifolds with vanishing Lee form.

Holomorphic tensors on Vaisman manifolds are invariant under the Lee field.

The Lee-Gauduchon cone is a convex cone of cohomology classes for complex manifolds.

Characterizes braid types and estimates twist coefficients.

The exterior derivative $d θ$ of the Lee form $θ$ of almost Hermitian manifolds is studied. If $ω$ is the Kähler two-form, it is proved that the $\mathbb{R}ω$-component of $dθ$ is always zero. expressions for the other components, in $[λ_0^{1,1}]$ and in $[[ λ^{2,0} ]]$, of $dθ$ are also obtained. They are given in ter…

Study on Lee classes of complex surfaces, proving connectedness and bounds.

Study negative band numbers in braids and links.

We study two kinds of transformation groups of a compact locally conformally Kahler (l.c.K.) manifold. First we study compact l.c.K. manifolds with parallel Lee form by means of the existence of a holomorphic l.c.K. flow. Next, we introduce the Lee-Cauchy-Riemann (LCR) transformations as a class of diffeomorphisms pres…

Integrable LCK manifolds characterized as Kähler Lie algebras.

The paper studies LCAK metrics on complex manifolds and their properties.

Article finds a geometric connection between structures on manifolds.

We establish a Hard Lefschetz Theorem for the de Rham cohomology of compact Vaisman manifolds. A similar result is proved for the basic cohomology with respect to the Lee vector field. Motivated by these results, we introduce the notions of a Lefschetz and of a basic Lefschetz locally conformal symplectic (l.c.s.) mani…

New insights on ACYT 6-manifolds reveal instanton conditions for curvature.

Lobb observed in [arXiv:1103.1412] that each equivariant sl(N) Khovanov-Rozansky homology over C[a] admits a standard decomposition of a simple form. In the present paper, we derive a formula for the corresponding Lee-Gornik spectral sequence in terms of this decomposition. Based on this formula, we give a simple alter…

We prove that any compact homogeneous locally conformally Kähler manifold has parallel Lee form.

Study on instantons in $G_2$ and $Spin(7)$ manifolds.

We compute the condition of minimality of a G-structure for the Gray-Hervella class $\mathcal{W}_4$ of almost hermitian manifolds and $\mathcal{C}_5$ class of almost contact metric structures. We also consider $\mathcal{C}_4$ class by comparison with the Grey-Hervella class $\mathcal{W}_4$. The common feature is the ex…

We give a short proof of the fact that compact pluricanonical locally conformally Kähler manifolds have parallel Lee form.

A locally conformally Kahler manifold is a Hermitian manifold $(M,I,ω)$ satisfying $dω=θ\wedge ω$, where $θ$ is a closed 1-form, called the Lee form of $M$. It is called pluricanonical if $\nablaθ$ is of Hodge type $(2,0)+(0,2)$, where $\nabla$ is the Levi-Civita connection, and Vaisman if $\nablaθ=0$. We show that a c…

We prove that the deRham cohomology classes of Lee forms of locally conformally symplectic structures taming the complex structure of a compact complex surface $S$ with first Betti number equal to $1$ is either a non-empty open subset of $H^1_{dR}(S, \mathbb R)$, or a single point. In the latter case, we show that $S$ …

Normalizes pseudo-Einstein contact forms for easier analysis.

We characterize compact locally conformally Kähler (l.c.K.) manifolds under the assumption of a purely conformal, holomorphic circle action. As an application, we determine the structure of the compact l.c.K. manifolds with parallel Lee form. We introduce the Lee-Cauchy-Riemann (LCR) transformations as a class of diffe…

Study second-Chern-Einstein metrics on 4D manifolds, finding Killing vector fields and examples.

We prove that a compact lcK manifold with holomorphic Lee vector field is Vaisman provided that either the Lee field has constant norm or the metric is Gauduchon (i.e., the Lee field is divergence-free). We also give examples of compact lcK manifolds with holomorphic Lee vector field which are not Vaisman.

The asymptotic behavior of the implied volatility associated with a general call pricing function has been extensively studied in the last decade. The main topics discussed in this paper are Lee's moment formulas for the implied volatility, and Piterbarg's conjecture, describing how the implied volatility behaves in th…

The study examines Lee metrics on groups and their properties.

We study the Euler-Lagrange equation for several natural functionals defined on a conformal class of almost Hermitian metrics, whose expression involves the Lee form $θ$ of the metric. We show that the Gauduchon metrics are the unique extremal metrics of the functional corresponding to the norm of the codifferential of…

We study the condition in which G2-structures are introduced by a non closed four-form, although they are satisfying locally conformal conditions.All solutions are found in the case when the Lee form of G2-structures is non-zero and gintroduces seven-dimensional Lie algebras, The main results are given in preposition1 …

Lee's work on twisted torus knots with Fibonacci parameters is extended to Horadam parameters.

We give a complete description of all locally conformally Kähler structures with holomorphic Lee vector field on a compact complex manifold of Vaisman type. This provides in particular examples of such structures whose Lee vector field is not homothetic to the Lee vector field of a Vaisman structure. More generally, dr…

n this paper, we obtain a geometric inequality between the length of the second fundamental form and the length of Lee form in terms of the warping function for a CR-warped product submanifold in a locally conformal Kaehler space form. The equality case is also investigated. Furthermore, the inequality is discussed for…

Lee homology (a variant of Khovanov homology) over $\mathbb{Q}$ possesses the "canonical generators" as its basis. The generators (Lee's classes) $[α(D, o)]$ are constructed combinatorially from an oriented link diagram $D$, one for each alternative orientation $o$ on $D$. Let $R$ be an integral domain. There exists a …

Study on higher order Levi forms on homogeneous CR manifolds, improving previous results.

A classification scheme of the conformal almost contact metric manifolds with respect to the covariant derivative of the Lee form is given. The subclasses of one basic class and their exact characterizations by the maximal subgroups of the contact conformal group preserving itself are found.

Garside's results and the existense of the greedy normal form for braids are shown to be true for the singular braid monoid. An analogue of the presentation of J. S. Birman, K. H. Ko and S. J. Lee for the braid group is also obtained for this monoid.

Synthetic proof of Gannon-Lee theorem for spacetimes.

Paper uses neural networks to calibrate Lee-Carter models for multiple populations.

Proves Gannon-Lee theorem for $C^1$ spacetimes.

Formula derived for Spin(7)-structures on 8D manifolds.

The paper counts ends of differential forms on surfaces.

In this article we use the combinatorial and geometric structure of manifolds with embedded cylinders in order to develop an adiabatic decomposition of the Hodge cohomology of these manifolds. We will on the one hand describe the adiabatic behaviour of spaces of harmonic forms by means of a certain Čech-de Rham complex…

We show that on an HKT manifold the holonomy of the Obata connection is contained in SL(n,H) if and only if the Lee form is an exact one form. As an application, we show compact HKT manifolds with holomorphically trivial canonical bundle which are not balanced. A simple criterion for non-existence of HKT metric on hype…

We discuss a remarkable formula discovered by Jerison and Lee to classify constant scalar curvature pseudohermitian structures on the sphere. We show that the formula is valid in the wider context of Einstein pseudohermitian manifolds. As an application we prove a uniqueness result that generalizes the theorem of Jeris…

We obtain conditions on the Lee form under which a holomorphic map between almost Hermitian manifolds is a harmonic map or morphism. Then we discuss under what conditions (i) the image of a holomorphic map from a cosymplectic manifold is also cosymplectic, (ii) a holomophic map with Hermitian image defines a Hermitian …

In this paper, we extend the classical Ho-Lee binomial term structure model to the case of time-dependent parameters and, as a result, resolve a drawback associated with the model. This is achieved with the introduction of a more flexible no-arbitrage condition in contrast to the one assumed in the Ho-Lee model.