arXiv 1306.28132013-06math.DGgr-qcmath-phmath.MP

Almost Kaehler Ricci Flows and Einstein and Lagrange-Finsler Structures on Lie Algebroids

Sergiu I. Vacaru

备注：: This version is accepted by Mediterranian J. Math. and modified following editor/referee's requests. File latex2e 11pt generates 29 pages
发表信息：: Mediterr. J. Math. 12 (2015) 1397-1427
DOI：: 10.1007/s00009-014-0461-7

英文摘要：

In this work we investigate Ricci flows of almost Kaehler structures on Lie algebroids when the fundamental geometric objects are completely determined by (semi) Riemannian metrics, or effective) regular generating Lagrange/ Finsler, functions. There are constructed canonical almost symplectic connections for which the geometric flows can be represented as gradient ones and characterized by nonholonomic deformations of Grigory Perelman's functionals. The first goal of this paper is to define such thermodynamical type values and derive almost Kähler - Ricci geometric evolution equations. The second goal is to study how fixed Lie algebroid, i.e. Ricci soliton, configurations can be constructed for Riemannian manifolds and/or (co) tangent bundles endowed with nonholonomic distributions modelling (generalized) Einstein or Finsler - Cartan spaces. Finally, there are provided some examples of generic off-diagonal solutions for Lie algebroid type Ricci solitons and (effective) Einstein and Lagrange-Finsler algebroids.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

非完整代数体、Finsler几何和Lagrange-Hamilton空间

Nonholonomic Algebroids, Finsler Geometry, and Lagrange-Hamilton Spaces

在具有非线性联络（N-联络）结构的李代数胚上，我们阐述了经典力学、Riemann-Finsler空间和引力理论的统一几何方法.研究了在力学模型中，锚、度规和线性联络、几乎辛和相关的几乎复结构等基本几何对象可以用正则拉格朗日量（或哈密顿量）导出的N-联络或引力理论中的一般非对角度规项和非完整标架正则地定义的条件。这样的几何结构是仿照非完整流形提供不可积的分布和相关链的确切序列的子流形定义N-连接。我们调查的主要性质的拉格朗日，汉密尔顿，芬斯勒-黎曼和爱因斯坦-嘉当代数胚和构造和分析精确的解决方案描述这样的对象。

2007-04-30gr-qchep-thmath-ph

Clifford-Finsler代数胚与非完整Einstein-Dirac结构

Clifford-Finsler Algebroids and Nonholonomic Einstein-Dirac Structures

本文提出了一个新的框架，用于构造同时具有Clifford-Lie代数体对称性和非线性联络结构的非完整流形上的几何和物理模型。一般非对角度量的显式参数化以及线性和非线性连接定义了不同类型的Finsler，Lagrange和/或Riemann-Cartan空间。非完整流形上的旋量场和狄拉克算子的推广激发了定义为Clifford丛的Clifford代数体理论，一般情况下，启用定义非线性连接的不可积分布。在这项工作中，我们阐述了代数体旋量微分几何和制定（标量，Proca，引力子，旋量和规范）场方程的李代数体。本文传达了物理理论的几何表述的新发展，这种方法是基于以前的一些例子，当精确解与通用非对角度量和广义对称性在现代引力定义非完整时空流形与非紧化额外的维度。

2006-08-09gr-qchep-thmath-ph

Finsler structures on holomorphic Lie algebroids

Complex Finsler vector bundles have been studied mainly by T. Aikou, who defined complex Finsler structures on holomorphic vector bundles. In this paper, we consider the more general case of a holomorphic Lie algebroid E and we introduce Finsler structures, partial and Chern-Finsler connections on it. First, we recall some basic notions on holomorphic Lie algebroids. Then, using an idea from E. Martinez, we introduce the concept of complexified prolongation of such an algebroid. Also, we study nonlinear and linear connections on the tangent bundle of E and on the prolongation of E and we inves…

2017-05-25math.DG

李代数胚上的Finsler几何模型

Models of Finsler Geometry on Lie algebroids

研究了李代数体延拓上的水平自同态、殆复结构、垂直提升、水平提升和完全提升。然后利用正合序列构造半投影。此外，还研究了李代数胚的延拓上的一些重要几何对象，如经典的特殊联络、挠和部分曲率。考虑回拉束，基于锚点映射研究了共变导数。李代数体结构的几个芬斯勒几何模型，将通过最近的论点组织。最后，对一些特殊的Finsler李代数体空间进行了改进.

2013-10-28math.DG

Geometrical structures on the prolongation of a pre-Lie algebroid on fibered manifolds and application to Partial Finsler geometry on foliated anchored bundle

A pre-Lie algebroid is an anchored bundle provided with an almost Lie bracket such that the anchor is compatible with the Lie bracket of vector fields. We firstly show how most geometrical structures intensively studied in the framework of Lie algebroid can easily be extended in the pre-Lie algebroid context. The principal purpose of this paper is to show that how all these results only depend of the foliated structure and do not depend of the pre-Lie algebroid structure that we can put on a foliated anchored bundle. As application, we obtain a Finsler connection on a foliated anchored bundle …

2016-06-08math.DG

Laplace operators on holomorphic Lie algebroids

The paper introduces Laplace-type operators for functions defined on the tangent space of a Finsler Lie algebroid, using a volume form on the prolongation of the algebroid. It also presents the construction of a horizontal Laplace operator for forms defined on the prolongation of the algebroid. All of the Laplace operators considered in the paper are also locally expressed using the Chern-Finsler connection of the algebroid.

2017-09-07math.DG

更多相关论文收起更多论文

广义李代数体上的拉格朗日力学

Lagrangian Mechanics on Generalized Lie Algebroids

本文的目的是在广义李代数胚的一般框架下求解Weinstein问题。我们提出了机械系统的使用，机械（？; ?)-系统，拉格朗日力学（？; ?)-系统或芬斯勒机械（？?)-我们发展它们的几何形状。我们得到了正则（？; ?)-半（喷雾）与机械（？; ?)-系统拉格朗日力学（？; ?)-系统是发展拉格朗日形式主义所必需的空间。我们得到了（？; ?)-半空间中的一个正则拉格朗日量L和一个外力Fe，导出了Euler-Lagrange型方程。对拉格朗日力学的经典和现代结果提出了新的看法。

2011-08-23math-phmath.DGmath.DS

非完整Clifford和Finsler结构、非交换Ricci流和数学相对论

Nonholonomic Clifford and Finsler Structures, Non-Commutative Ricci Flows, and Mathematical Relativity

本文概述了作者18年来在数学物理、粒子物理和引力中的几何方法、修正和应用等方面的研究活动（1994年博士论文答辩后）。十个最相关的出版物按常规结构分为三个“战略方向”：1）非完整几何流的演化和Ricci孤子和场方程的精确解，（2）非线性动力学和各向异性场相互作用模型量子化的几何方法;（3）（非）交换几何，几乎Kaehler和Clifford结构，Dirac算子和有效的Lagrange-Hamilton和Riemann-Finsler空间。

2012-04-21math-phmath.DGmath.MP

Courant代数胚上度量结构的约化

Reduction of metric structures on Courant algebroids

利用Courant代数胚的约化过程，约化了Courant代数胚上的强KT结构、超KT结构和广义Kaehler结构.这使我们能够从文献中恢复结果，并从不同的角度解释其中观察到的一些特征。作为一个例子，我们证明了SKT/HKT/广义Kähler流形上丛的瞬子的模空间具有与原流形相同的结构.

2012-03-02hep-thmath.DG

李代数体广义切丛的度量化与（广义）Lagrange $(ρ,η)$ -空间

Metrizability of the Lie algebroid generalized tangent bundle and (generalized) Lagrange $(ρ,η)$-spaces

在广义李代数胚的一般框架下，一类可度量化的向量丛已在八篇文献中得到了证明。利用广义李代数胚得到了向量丛的广义切丛.这个李代数胚是可度量化向量丛的一个新例子。一类新的Lagrange空间，称为广义Lagrange（ρ？;η？）-空间，Lagrange（ρ？;η？）-空间和Finsler（ρ？;η？）-空间呈现。在李代数胚的特殊情况下，新的和重要的结果。特别地，如果所有态射都是恒等态射，则得到了经典结果。

2013-08-14math.DG

瞬子模空间的广义Kaehler几何

Generalized Kaehler geometry of instanton moduli spaces

本文证明了紧致偶广义Kaehler四流形上瞬子模空间的Hitchin广义Kaehler结构可通过广义Kaehler约化获得，其底层Courant algebroid约化实现了Donaldson三次$μ$-映射。

2013-08-19hep-thmath.DGmath.SG

Symmetric brackets induced by connections with totally skew-symmetric torsion on skew-symmetric algebroids

In this note, we discuss symmetric brackets on skew-symmetric algebroids associated with a metric structure. Given a pseudo-Riemannian metric structure, we describe symmetric brackets induced by connections with totally skew-symmetric torsion in the language of Lie derivatives and differentials of functions. In particular, we obtain an explicit formula of the Levi-Civita connection. We also present some symmetric brackets on almost Hermitian manifolds. Especially, we discuss the first canonical Hermitian connection and show the formula for it in the case of nearly Kaehler manifolds using the p…

2020-12-17math.DG

Connections in holomorphic Lie algebroids

The main purpose of this note is the study of the total space of a holomorphic Lie algebroid $E$. The paper is structured in three parts. In the first section we briefly introduce basic notions on holomorphic Lie algebroids. The local expressions are written and the complexified holomorphic bundle is introduced. The second section is a little broader and includes two approaches to study the geometry of complex manifold $E.$ The first part contains the study of the tangent bundle $T_{C}E=T^{\prime }E\oplus T^{\prime \prime }E$ and its link, via tangent anchor map, with the complexified tangent …

2016-05-26math.DG

广义黎曼流形上的Dirac结构

Dirac structures on generalized Riemannian manifolds

我们刻画了广义黎曼度量的与Gualtieri正则联络平行的Dirac结构。另一方面，我们讨论的狄拉克结构是广义切结构的图像。这些结构原来是狄拉克结构，如果被视为李代数胚，有一个辛结构。特别地，如果需要与广义黎曼度量相容，则辛结构是Kaehler型的。

2011-05-30math.DGmath.SG