A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper examines metrics on foliated manifolds that have special geometric properties.
New spectral sequence for -manifolds, computing cohomology and harmonic forms.
In this paper, we consider a Riemannian foliation whose normal bundle carries a parallel or harmonic basic form. We estimate the norm of the O'Neill tensor in terms of the curvature data of the whole manifold. Some examples are then given.
On a compact foliated Riemannian manifold with some transversal curvature conditions, there are no nontrivial basic harmonic forms (M. Min-Oo et al., J. Reine Angew. Math. 415 (1991). In this paper, we extend the above facts to a complete foliated Riemannian manifold.
The abstract discusses p-harmonic forms and their geometric properties, proving new theorems about Lp-cohomology.
We introduce the study of nonlinear harmonic forms. These are forms which minimize the energy in a cohomology class subject to a nonlinear constraint. In this note, we include only motivations and the most basic existence results. We also introduce a variant of the Bochner formula suitable for probing the structu…
We study basic Dolbeault cohomology and find new Weitzenböck formulas on a transversely Kähler foliation. We investigate conditions on mean curvature and Ricci curvature that impose restrictions on basic Dolbeault cohomology. For example, we prove that on a transversely Kähler foliation with positive transversal Ricci …
Study on twisted Dolbeault cohomology in Kähler foliations.
In this paper we introduce higher extremal Kahler metrics. We provide an example of the same on a minimal ruled surface. We also prove a perturbation result that implies that there are non-trivial examples of higher constant scalar curvature metrics, which are basically metrics where the top Chern form is harmonic. We …
A stochastic flow is constructed on a frame bundle adapted to a Riemannian foliation on a compact manifold. The generator A of the resulting transition semigroup is shown to preserve the basic functions and forms, and there is an essentially unique strictly positive smooth function phi satisfying A^* phi = 0. This func…
Explains Hodge theory and Kodaira embedding theorem for complex manifolds.
This paper studies gradient almost Ricci-harmonic soliton with respect to a fixed metric. We rely on analytic techniques to estabilish some basic elliptic and integral equations for the structure of almost Ricci-harmonic soliton which generalizes that of Ricci-hamonic solitons on one hand and that of almost Ricci solit…
Using basic homotopy constructions, we show that isomorphism classes of string structures on spin bundles are naturally given by certain degree 3 cohomology classes, which we call string classes, on the total space of the bundle. Using a Hodge isomorphism, we then show that the harmonic representative of a string class…
In this paper, we give some rigidity results for both harmonic and pseudoharmonic maps from CR manifolds into Riemannian manifolds or Kahler manifolds. Some basicity, pluriharmonicity and Siu-Sampson type results are established for both harmonic maps and pseudoharmonic maps.
New classification for Vaisman manifolds with specific properties.
In this note, we show that for any harmonic map into a non-compact symmetric space one can find naturally a "dual" harmonic map into a compact symmetric space which can be constructed from the same basic data (called "potentials" in the loop group formalism). Locally also the inverse/converse duality theorem holds.
The period is a classical complex analytic invariant for a compact Riemann surface defined by integration of differential 1-forms. It has a strong relationship with the complex structure of the surface. In this chapter, we review another complex analytic invariant called the harmonic volume. It is a natural extension o…
The title is self-explanatory. We aim to give an easy to read and self-contained introduction to the field of harmonic manifolds. Only basic knowledge of Riemannian geometry is required. After we gave the definition of harmonicity and derived some properties, we concentrate on Z. I. Szabó's proof of Lichnerowicz's conj…
Motivated from the action functional for bosonic strings with extrinsic curvature term we introduce an action functional for maps between Riemannian manifolds that interpolates between the actions for harmonic and biharmonic maps. Critical points of this functional will be called interpolating sesqui-harmonic maps. In …
In this article we present an intrinsec construction of foliated Brownian motion via stochastic calculus adapted to foliation. The stochastic approach together with a proposed foliated vector calculus provide a natural method to work on harmonic measures. Other results include a decomposition of the Laplacian in terms …
The paper investigates Liouville type theorems for various harmonic forms on Riemannian manifolds.
We show that, in quaternionic geometry, the Ward transform is a manifestation of the functoriality of the basic correspondence between the -quaternionic manifolds and their twistor spaces. We apply this fact, together with the Penrose transform, to obtain existence results for hypercomplex manifolds and for harmonic…
New metrics produce discrete zero sets for nondegenerate harmonic forms.
The study resolves a conjecture about harmonic forms on compact manifolds.
Recalls intrinsically harmonic forms and open problems.
In this paper we study a class of functions that appear naturally in some equidistribution problems and that we call -harmonic. These are functions of the universal cover of a closed and negatively curved which possess an integral representation analogous to the Poisson representation of harmonic functions, where th…
The study examines harmonic forms on almost Hermitian manifolds and complex surfaces.
Criterion for flat circle bundles using intrinsically harmonic forms.
Study primitive decompositions for harmonic forms on almost Kähler manifolds.
The study calculates harmonic functions and 1-forms on specific 4D spaces.
The paper proves vanishing and finiteness theorems for p-harmonic 1-forms.
The study finds nondegenerate harmonic 1-forms using symmetry conditions.
Conditions for a soliton's dual form to be harmonic or Ricci harmonic are derived.
We consider interpolating sesqui-harmonic Legendre curves in Sasakian space forms. We find the necessary and sufficient conditions for Legendre curves in Sasakian space forms to be interpolating sesqui-harmonic. Finally, we obtain an example for an interpolating sesqui-harmonic Legendre curve in a Sasakian space form.
We characterize the harmonic forms on a flag manifold defined by Kostant in 1963 in terms of a Poisson structure. Namely, they are ``Poisson harmonic" with respect to the so-called Bruhat Poisson structure on . This enables us to give Poisson geometrical proofs of many of the special properties of these harm…
Symmetry operators of twistor spinors and harmonic spinors can be constructed from conformal Killing-Yano forms. Transformation operators relating twistors to harmonic spinors are found in terms of potential forms. These constructions are generalized to gauged twistor spinors and gauged harmonic spinors. The operators …
In general, the product of harmonic forms is not harmonic. We study the top exterior power of harmonic two-forms on compact Kaehler manifolds. Often, it is not harmonic. This phenomenon is related to the geometry of the manifold and to the existence of rational curves in particular. K3 surfaces and hyperkaehler manifol…
The paper constructs harmonic 1-forms on 3-manifolds with cylindrical necks.
Study metric perturbations to make degenerate harmonic forms non-degenerate.
Study -harmonic forms on almost Kähler manifolds, extending vanishing theorems.
Analyzes -harmonic forms on curved manifolds, proving integrability conditions.
Novel singularity models for 4D harmonic forms and spinors from polytopes.
P. Baird and the second author studied harmonic morphisms from a three-dimensional simply-connected space form to a surface and obtained a complete local and global classification of them. In this paper, we obtain a description of all harmonic morphisms from any three-dimensional Euclidean and spherical space form to a…
Harmonic forms and Rumin complex linked on Sasakian manifolds.
New examples of Z/2 harmonic 1-forms and their branching sets are explored.
The paper introduces new cohomologies and studies harmonic forms on almost complex manifolds.
We prove that manifolds admitting a Riemannian metric for which products of harmonic forms are harmonic satisfy strong topological restrictions, some of which are akin to properties of flat manifolds. Others are more subtle, and are related to symplectic geometry and Seiberg-Witten theory. We also prove that a manifold…
Study on harmonic forms on K3 surfaces converging to a flat 4D orbifold.