Local Dynamics of Conformal Vector Fields

Charles Frances

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Local Dynamics of Conformal Vector Fields

Charles Frances

Differential Geometry · Submitted 1 Sep 2009

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

The authors' main claim We begin a general study in this direction, for any pseudo-Riemannian type, and give a complete answer in the Riemannian case.

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What the abstract itself states, as probabilities: claims first 0.14 · states limitation 0.53 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.05 · mentions code or data availability 0.01.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

The aim of the paper is to understand the local forms of conformal vector fields in the neighborhood of a singularity. We begin a general study in this direction, for any pseudo-Riemannian type, and give a complete answer in the Riemannian case. This is done using geometric methods, and studying local dynamics of sequences of conformal transformations.

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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	The aim of the paper is to understand the local forms of conformal vector fields in the neighborhood of a singularity.	background 0.77	0.24	0.04	asserted 0.75
s1	We begin a general study in this direction, for any pseudo-Riemannian type, and give a complete answer in the Riemannian case.	contribution 0.94	0.92	0.34	asserted 1.00
s2	This is done using geometric methods, and studying local dynamics of sequences of conformal transformations.	method 1.00	0.87	0.07	asserted 0.98

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

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arXiv listing abstract v2

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The paper

Original abstract

The aim of the paper is to understand the local forms of conformal vector fields in the neighborhood of a singularity. We begin a general study in this direction, for any pseudo-Riemannian type, and give a complete answer in the Riemannian case. This is done using geometric methods, and studying local dynamics of sequences of conformal transformations.

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5 arXiv papers cite this in 12 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 · 8 sentences without a confident label

Builds on it 1 paper

Then, we apply the identity reviewed in Section [ref] to prove a generalization of results of [ref] , which give a “dictionary” relating essentiality of an infinitesimal automorphism near a singularity $x_0$ to properties of its holonomy $h^t$ at $x_0$, a one-parameter subgroup of $P$ which is determined up to conjugacy (cf. Definition [ref]; it should be emphasized that this notion of “holonomy” of the singularity of an infinitesimal automorphism is distinct from the holonomy of, e.g., a Cartan connection which is common in the literature).

Essential Parabolic Structures and Their Infinitesimal Automorphisms · Organization of the text and summary of main results · 0.96

Uses its method or tool 1 paper

I am grateful to Charles Frances for discussions about the methods used in [ref] and [ref] , and to Felipe Leitner for useful comments on an earlier version of the text.

Essential Parabolic Structures and Their Infinitesimal Automorphisms · Acknowledgements · 0.97

Cites it as support 1 paper

Now, the lemma follows from the fact that conformal geodesics developping on short curves in $$ are themselves short ( [ref] ), and that conformal geodesics of $$ which are Hausdorff-close to $ν$ must be short ( [ref] ).

Removable and essential singular sets for higher dimensional conformal maps · Degeneration of conformal cones · 0.96

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