等仿射膜世界
Equiaffine braneworld
摘要：
高维理论，其中我们的四维宇宙沉浸在一个大的环境，最近受到了很大的关注，调查的方向，据我们所知，都遵循普通的欧几里得超曲面理论的等距沉浸配方，时空度规是由周围的父母引起的。我们在本文中注意到，洛伦兹度规的不确定签名可能暗示了鲜为人知的等仿射超曲面理论可能是一个更自然的，即，除了最低限度的数学形式主义，我们宇宙的外在几何的描述。在这个替代方案中，环境失去了度规，时空度规变得与普通理论的第二基本形式共形，因此对于双曲形状自动是不确定的。在这里，我们主张在这个方向上的调查，确定一些潜在的物理利益，争取帮助等仿射微分几何。
英文摘要：
Higher dimensional theories, wherein our four dimensional universe is immersed into a bulk ambient, have received much attention recently, and the direction of investigation had, as far as we can discern, all followed the ordinary Euclidean hypersurface theory's isometric immersion recipe, with the spacetime metric being induced by an ambient parent. We note in this paper that the indefinite signature of the Lorentzian metric perhaps hints at the lesser known equiaffine hypersurface theory as being a possibly more natural, i.e., less customized beyond minimal mathematical formalism, description of our universe's extrinsic geometry. In this alternative, the ambient is deprived of a metric, and the spacetime metric becomes conformal to the second fundamental form of the ordinary theory, therefore is automatically indefinite for hyperbolic shapes. Herein, we advocate investigations in this direction by identifying some potential physical benefits to enlisting the help of equiaffine differential geometry.
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