Generalized Calabi-Yau metric and Generalized Monge-Ampere equation

Chris M. Hull; Martin Rocek; Maxim Zabzine; Rikard von Unge; Ulf Lindstrom

RECORD

Generalized Calabi-Yau metric and Generalized Monge-Ampere equation

Chris M. Hull, Ulf Lindstrom, Martin Rocek, Rikard von Unge, Maxim Zabzine

High Energy Physics - Theory · Submitted 31 May 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We study the local conditions for a generalized Kahler manifold to be a generalized Calabi-Yau manifold and we derive a non-linear PDE that the generalized Kahler potential has to satisfy for this to be true.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

arXiv ID1005.5658 (version 1)

Pith IDF4BPRHER, Pith's permanent record of this paper and its review

CitationChris M. Hull, Martin Rocek, Maxim Zabzine, Rikard von Unge, Ulf Lindstrom. "Generalized Calabi-Yau metric and Generalized Monge-Ampere equation." arXiv:1005.5658 (2010). https://pith.science/paper/F4BPRHER

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,994 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.16 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

In the neighborhood of a regular point, generalized Kahler geometry admits a description in terms of a single real function, the generalized Kahler potential. We study the local conditions for a generalized Kahler manifold to be a generalized Calabi-Yau manifold and we derive a non-linear PDE that the generalized Kahler potential has to satisfy for this to be true. This non-linear PDE can be understood as a generalization of the complex Monge-Ampere equation and its solutions give supergravity solutions with metric, dilaton and H-field.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In the neighborhood of a regular point, generalized Kahler geometry admits a description in terms of a single real function, the generalized Kahler potential.	background 1.00	0.14	0.05	asserted 0.97
s1	We study the local conditions for a generalized Kahler manifold to be a generalized Calabi-Yau manifold and we derive a non-linear PDE that the generalized Kahler potential has to satisfy for this to be true.	contribution 0.95	0.96	0.52	asserted 1.00
s2	This non-linear PDE can be understood as a generalization of the complex Monge-Ampere equation and its solutions give supergravity solutions with metric, dilaton and H-field.	interpretation 0.90	0.78	0.58	asserted 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

In the neighborhood of a regular point, generalized Kahler geometry admits a description in terms of a single real function, the generalized Kahler potential. We study the local conditions for a generalized Kahler manifold to be a generalized Calabi-Yau manifold and we derive a non-linear PDE that the generalized Kahler potential has to satisfy for this to be true. This non-linear PDE can be understood as a generalization of the complex Monge-Ampere equation and its solutions give supergravity solutions with metric, dilaton and H-field.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

8 arXiv papers cite this in 23 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 14 sentences without a confident label

Compares with it 1 paper

([ref]) and ([ref]) and $Ξ^±$ are given by, [equation] The expressions for the pure spinors appear differently from those in [ref] but they are actually the same (except for complex conjugation).

The generalized Kaehler geometry of N=(2,2) WZW-models · Supersymmetric $σ$-models in $N=(2,2)$ superspace · 0.97

Cites it as background 5 papers

The generalized Calabi-Yau conditions on the generalized Kähler potential in $N=(2,2)$ superspace language were studied in [ref] .

The generalized Kaehler geometry of N=(2,2) WZW-models · Discussion and conclusions · 0.96
The conditions for conformal invariance of the NLSM at the quantum level, and the relation to the generalized Calabi-Yau condition of Hitchin [ref] , is discussed in [ref] .

On gauged linear sigma models with torsion · Comment on RG Flow · 0.98
The conditions for conformal invariance at the quantum level, and the relation to the generalized Calabi-Yau condition of Hitchin [ref] , is discussed in [ref] .

Semichiral Fields on S^2 and Generalized K\"ahler Geometry · Introduction · 0.97

What it cites · 17 sentences without a confident label

Compares with 1 paper

Taking the logarithm of the left hand side of ([ref]) we get exactly the $N=(2,2)$ superspace counterterm calculated in [ref] .

The Quantum Geometry of N=(2,2) Non-Linear Sigma-Models · Physical interpretation · 0.89

Cites as support 3 papers

Through the theorem in [ref] we know that the existence of a pair of compatible closed pure spinors implies the existence of supersymmetric supergravity solutions.

Generalised $G_2$-structures and type IIB superstrings · Generalized and Calabi-Yau geometries · 0.96
Through the theorem in [ref] we know that the existence of a pair of compatible closed pure spinors implies the existence of supersymmetric supergravity solutions.

Metric bundles of split signature and type II supergravity · Generalized and Calabi-Yau geometries · 0.96
J_+ J_- + J_- J_+ =2 ( 1-α/1+α ) 𝕀 and, as shown in [ref] , when $( 1-α/1+α )^2<1$ (which is true since $α$ is positive), it is possible to explicitly construct a hyperstructure so the geometry is hyper.

Generalized Kahler manifolds and off-shell supersymmetry · Symplectic case: $d_c = d_t =0$ · 0.97

Cites as background 13 papers

We follow Gualtieri's terminology [ref] .] is defined as a pair of closed pure spinors $ρ_1$ and $ρ_2$ such that the corresponding generalized complex structures $J_1$ and $J_2$ give rise to a generalized structure and moreover that $(ρ_1, ρ̅_1) = α(ρ_2, ρ̅_2)≠0$ for some non-zero constant $α$.

math.DG/0401221 · Generalized and Calabi-Yau geometries · 0.84
Hitchin in [ref] has attracted considerable interest in both physics and mathematics.

math.DG/0209099 · Introduction · 1.00
For further detail on the local description of generalized geometry and its relation to supersymmetric sigma models the reader may consult [ref] .

A potential for Generalized Kahler Geometry · Summary · 1.00

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.