论文标题
迈向共形超表面不变的分类
Toward a Classification of Conformal Hypersurface Invariants
论文作者
论文摘要
嵌入在保形歧管中的高空曲面在宇宙学和字符串理论中经常以边界数据的边界数据出现。我们被视为时空的非无效保形无穷大，我们认为嵌入了riemannian（或Lorentzian）保形的歧管中的超曲面。我们构建了一个有限且最小的高度表面张量家族 - 高浮力的曲率和所谓的``共同基本形式''固有的 - 可用于构建嵌入到固定的固定词的固定顺序的高度序列的自然保形不变性，以构建固定量的固定顺序 - 正态 - 正态衍生物的固定量。因此，我们表明这些保形基本形式捕获了时空中形式的共形无穷大的外部嵌入数据。
Hypersurfaces embedded in conformal manifolds appear frequently as boundary data in boundary-value problems in cosmology and string theory. Viewed as the non-null conformal infinity of a spacetime, we consider hypersurfaces embedded in a Riemannian (or Lorentzian) conformal manifold. We construct a finite and minimal family of hypersurface tensors -- the curvatures intrinsic to the hypersurface and the so-called ``conformal fundamental forms'' -- that can be used to construct natural conformal invariants of the hypersurface embedding up to a fixed order in hypersurface-orthogonal derivatives of the bulk metric. We thus show that these conformal fundamental forms capture the extrinsic embedding data of a conformal infinity in a spacetime.
