Deformation of the Weighted Scalar Curvature

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-11-04 DOI:10.3842/sigma.2023.087

Pak Tung Ho, Jinwoo Shin

引用次数: 0

Abstract

Inspired by the work of Fischer-Marsden [Duke Math. J. 42 (1975), 519-547], we study in this paper the deformation of the weighted scalar curvature. By studying the kernel of the formal $L_\phi^2$-adjoint for the linearization of the weighted scalar curvature, we prove several geometric results. In particular, we define a weighted vacuum static space, and study locally conformally flat weighted vacuum static spaces. We then prove some stability results of the weighted scalar curvature on flat spaces. Finally, we consider the prescribed weighted scalar curvature problem on closed smooth metric measure spaces.

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加权标量曲率的变形

受fisher - marsden(杜克数学)的启发。[j] . 42(1975)， 519-547]，本文研究了加权标量曲率的变形。通过研究加权标量曲率线性化的形式$L_\phi^2$伴随的核，证明了几个几何结果。特别地，我们定义了一个加权真空静态空间，并研究了局部共形平坦加权真空静态空间。然后证明了平面空间上加权标量曲率的一些稳定性结果。最后，我们考虑了闭光滑度量测度空间上的规定加权标量曲率问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.