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.
Introduces new deformation classes in generalized Kähler geometry.
The abstract discusses how generalized Calabi-Gray manifolds help solve non-Kähler geometry questions.
We introduce and study the notion of a biholomorphic gerbe with connection. The biholomorphic gerbe provides a natural geometrical framework for generalized Kahler geometry in a manner analogous to the way a holomorphic line bundle is related to Kahler geometry. The relation between the gerbe and the generalized Kahler…
Develops scalar curvature in generalized Kahler geometry and shows constant scalar curvature on compact Lie groups.
This work is based on the talk delivered at Poisson 2008. We review the recent advances in Generalized Kahler geometry while stressing the use of Poisson and symplectic geometry. The derivation of the generalized Kahler potential is sketched and the relevant global issues are discussed.
Generalized Kahler geometry is the natural analogue of Kahler geometry, in the context of generalized complex geometry. Just as we may require a complex structure to be compatible with a Riemannian metric in a way which gives rise to a symplectic form, we may require a generalized complex structure to be compatible wit…
It is known that the scalar curvature arises as the moment map in Kahler geometry. In pursuit of this analogy, we introduce the notion of a moment map in generalized Kahler geometry which gives the definition of a generalized scalar curvature on a generalized Kahler manifold. From the viewpoint of the moment map, we ob…
We give a physical derivation of generalized Kahler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri regarding the equivalence between generalized Kahler geometry and the bi-hermitean geometry of Gates-Hull-Rocek. When cast in the language of supersymmetri…
The geometry of the target space of an N=(2,2) supersymmetry sigma-model carries a generalized Kahler structure. There always exists a real function, the generalized Kahler potential K, that encodes all the relevant local differential geometry data: the metric, the B-field, etc. Generically this data is given by nonlin…
In the same way that a contact manifold determines and is determined by a symplectic cone, a Sasaki manifold determines and is determined by a suitable Kahler cone. Kahler-Sasaki geometry is the geometry of these cones. This paper presents a symplectic action-angle coordinates approach to toric Kahler geometry and how …
New submersions found in nearly Kähler geometry.
We prove a general result about the geometry of holomorphic line bundles over Kahler manifolds.
We review the information geometry of linear systems and its application to Bayesian inference, and the simplification available in the Kähler manifold case. We find conditions for the information geometry of linear systems to be Kähler, and the relation of the Kähler potential to information geometric quantities such …
We study the Kähler geometry of stage n Bott manifolds, which can be viewed as -dimensional generalizations of Hirzebruch surfaces. We show, using a simple induction argument and the generalized Calabi construction from [ACGT04,ACGT11], that any stage n Bott manifold admits an extremal Kähler metric. We also g…
This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)kähler reduction; projective superspace; the generalized Legendre construction; generalized Kähler geometry and constructions of hyperkähler metrics on Hermitean symmetri…
Futaki invariant vanishes on Hopf manifolds.
Local equivalence found between certain solitons and generalized Kähler-Ricci solitons.
The paper connects Kähler-Ricci shrinkers to Fano fibrations in algebraic geometry.
We present some fundamental facts about a class of generalized Kähler structures defined by invariant complex structures on compact Lie groups. The main computational tool is the BH-to-GK spectral sequences that relate the bi-Hermitian data to generalized geometry data. The relationship between generalized Hodge decomp…
Uniform K-stability ensures existence of special metrics on toric manifolds.
We show that, locally, all geometric objects of Generalized Kahler Geometry can be derived from a function K, the "generalized Kahler potential''. The metric g and two-form B are determined as nonlinear functions of second derivatives of K. These nonlinearities are shown to arise via a quotient construction from an aux…
In this lecture, we review some of the concepts of generalized geometry, as introduced by Hitchin and developed in the speaker's thesis. We also prove a Hodge decomposition for the twisted cohomology of a compact generalized Kähler manifold, as well as a generalization of the -lemma of Kähler geometry.
New ansatz for generalized Kähler surfaces derived from hyperKähler ansatz.
We show that our earlier work in \cite{LT05} extends to the twisted case, that is, we defined a notion of moment map and reduction in both twisted generalized complex geometry and twisted generalized Kähler geometry.
The paper studies a generalized Pythagorean theorem on dually flat spaces via toric geometry.
Extends finite entropy measures in Kähler geometry.
We continue the study of blow-ups in generalized complex geometry with the blow-up theory for generalized Kähler manifolds. The natural candidates for submanifolds to be blown-up are those which are generalized Poisson for one of the two generalized complex structures and can be blown up in a generalized complex manner…
Derives scalar curvature formula in generalized Kähler geometry.
We define the notion of a moment map and reduction in both generalized complex geometry and generalized Kähler geometry. As an application, we give very simple explicit constructions of bi-Hermitian structures on $\C¶^n$, Hirzebruch surfaces, the blow up of $\CP^2$ at arbitrarily many points, and other toric varieties,…
We prove the correspondence between the information geometry of a signal filter and a Kähler manifold. The information geometry of a minimum-phase linear system with a finite complex cepstrum norm is a Kähler manifold. The square of the complex cepstrum norm of the signal filter corresponds to the Kähler potential. The…
Survey of recent metric geometry in Kähler metrics space.
The paper generalizes inequalities on almost Kähler manifolds.
The paper studies automorphisms of generalized Kähler manifolds and their Lie algebras.
Unified Schwarz lemma in Kähler and Hermitian geometry.
Using toric geometry we give an explicit construction of the compact steady solitons for pluriclosed flow first constructed in arXiv:1802.00170. This construction also reveals that these solitons are generalized Kähler in two distinct ways, with vanishing and nonvanishing Poisson structure. This gives the first example…
We study Riemannian geometry of canonical Kahler-Einstein currents on projective Calabi-Yau varieties and canonical models of general type with crepant singularities. We prove that the metric completion of the regular part of such a canonical current is a compact metric length space homeomorphic to the original project…
This paper solves the generalized Kähler problem by linking it to symplectic geometry.
We extend harmonic map techniques to the setting of more general differential equations in conformal geometry. We obtain an extension of Siu's rigidity to Kahler-Weyl geometry and apply the latter to Vaisman's conjecture. Other applications include topological obstructions to the existence of Kahler-Weyl structures. Fo…
The study of real Einstein submanifolds in Kähler geometry.
Quantizes geodesics in Kähler and Sasaki geometry.
Constructs hyper-Kähler models using Riemann-Hilbert problems.
Strong Kähler with Torsion is the target space geometry of and supersymmetric nonlinear sigma models. We discuss how it can be represented in terms of Generalised Complex Geometry in analogy to the Gualtieri map from the geometry of supersymmetric nonlinear sigma models to Generalised Kähler Geo…
Solves generalized Kähler Calabi-Yau problem on compact manifolds.
Study global geometry of toric nearly Kähler manifolds using multi-moment maps.
Paper solves open problem in complex Finsler geometry.
Study classifies gravitational instantons based on their asymptotic geometry.
Study variational problems in Kähler geometry to construct metrics.
Study of complex 3-folds with vanishing Bismut Ricci form via special Kähler geometry.