Liouville's Theorem in Conformal Geometry
TL;DR: In this article, it was shown that conformal mappings of semi-Riemannian manifolds preserving pointwise the Ricci tensor are essentially of the same type as in the classical case but they can exist for metrics different from the Euclidean metric.
read more
About: This article is published in Journal de Mathématiques Pures et Appliquées. The article was published on 01 Sep 2007. and is currently open access. The article focuses on the topics: Conformal geometry & Conformal symmetry.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
•Book
Digital Simulation in Electrochemistry
Dieter Britz
- 22 Dec 2012
TL;DR: In this paper, the Explicit Method and the Explicit Methods of the Implicit Methods are discussed, as well as several other methods, such as adorption and convection of two-dimensional systems.
621
•Proceedings Article
Möbius Transformation for Fast Inner Product Search on Graph
Zhixin Zhou,Shulong Tan,Zhaozhuo Xu,Ping Li +3 more
- 01 Dec 2019
TL;DR: This work proposes a simple but novel graph indexing and searching algorithm to find the optimal solution with the largest inner product with the query based on the property that Mobius transformation introduces an isomorphism between a subgraph of l^2-Delaunay graph and Delaunaygraph for inner product.
•Posted Content
Finsler conformal Lichnerowicz-Obata conjecture
TL;DR: In this article, the Finsler analog of the conformal Lichnerowicz-Obata conjecture was shown to be a homothetic vector field of a Minkowski metric.
35
•Posted Content
Local Dynamics of Conformal Vector Fields
TL;DR: In this article, the authors studied the local forms of conformal vector fields in the neighborhood of a singularity for any pseudo-Riemannian type and gave a complete answer in the Riemannians case.
16
Huygens triviality of the time-independent Schr\"odinger equation. Applications to atomic and high energy physics
TL;DR: In this paper, it was shown that the Schrodinger equation with the time-independent Hamiltonian belongs to the equivalence class of Huygens triviality, a concept invented by Jacques Hadamard, which connects the 2nd order partial differential equations which are transformable into the wave equation.
7
References
Conformal Structures and Möbius Structures
Ravi S. Kulkarni
- 01 Jan 1988
TL;DR: Dombrowski et al. as mentioned in this paper showed that the conformai maps among the surfaces have far more flexibility than for example the isometries among surfaces, or line-preserving maps among planar domains.
Closed conformal vector fields on pseudo-Riemannian manifolds
TL;DR: A geometric proof of the existence of certain local coordinates on a pseudo-Riemannian manifold admitting a closed conformal vector field is given.