标题： 保里安类型-I模型在共形引力中的哈密顿表述和精确解 显示英文标题

标题： Hamiltonian Formulation and Exact Solutions of Bianchi type-I Model in Conformal Gravity

摘要： 我们开发了Bianchi类型-I宇宙模型在共形引力中的哈密顿形式，即由一个拉格朗日量描述的理论，该拉格朗日量包含从Weyl张量构造的二次曲率不变量，在四维空间中。我们推导出超哈密顿量和表达理论共形不变性的约束的显式形式，并写出正则方程组。为了寻找该系统的精确解，我们在正则变量上添加额外的约束，并通过一个全局归约算法，可能使约束代数闭合。这使我们能够提取所有可能以闭合解析形式书写的特定解。另一方面，探测局部解析结构，我们表明该系统不具有Painleve性质（存在可移动对数），因此不可积。我们强调了与局部可积性相关的方法如Painleve测试和全局技术如归约算法之间非常有益的相互作用。严格来说，我们证明了全局归约算法在寻找精确解的搜索中已被证明是全面的。突出显示了解与爱因斯坦空间的共形关系或缺乏这种关系。 显示英文摘要

摘要： We develop a Hamiltonian formulation of Bianchi type-I cosmological model in conformal gravity, i.e. the theory described by a Lagrangian which involves the quadratic curvature invariant constructed from the Weyl tensor, in four dimensions. We derive the explicit forms of the super-Hamiltonian and the constraint expressing the conformal invariance of the theory, and we write down the system of canonical equations. To seek out exact solutions to this system we add extra constraints on the canonical variables and we go through a global involution algorithm that possibly leads to the closure of the constraint algebra. This enables us to extract all possible particular solutions that may be written in closed analytical form. On the other hand, probing the local analytical structure we show that the system does not possess the Painleve property (presence of movable logarithms) and that it is therefore not integrable. We stress that there is a very fruitful interplay of local integrability-related methods such as the Painleve test and global techniques such as the involution algorithm. Strictly speaking, we demonstrate that the global involution algorithm has proven to be exhaustive in the search for exact solutions. The conformal relationship of the solutions, or absence thereof, with Einstein spaces is highlighted.