Laplace算子在1-形式上的限制：从$\mathbb{R}^{n+2}$和$\mathbb{R}^{n+1}$周围空间到嵌入的（A）dS $_n$子流形
Restriction of Laplace operator on one-forms: from $\mathbb{R}^{n+2}$ and $\mathbb{R}^{n+1}$ ambient spaces to embedded (A)dS$_n$ submanifolds
摘要：
在$\mathbb{R}^{n+2}$或$\mathbb{R}^{n+1}$空间中作用于一种形式的$a$：$\square a$的Laplace-de Rham算子被限制为$n$维伪球。这尤其包括$n$维德西特和反德西特时空。该限制被设计为提取相应的$n$维Laplace-de Rham算子作用于相应的伪球上的$n$维1-形式。在每种情况下，这两个运营商的显式公式。本文还研究了由Laplace-de Rham算子与附加项之和构成的$n$维算子到周围空间的逆问题.证明了对于任意附加项，嵌入空间上的该算子都是嵌入空间上Laplace-de Rham算子的限制，并利用Weitzenböck公式将这些结果转化为Laplace-Beltrami算子，给出了证明.
英文摘要：
The Laplace-de Rham operator acting on a one-form $a$: $\square a$, in $\mathbb{R}^{n+2}$ or $\mathbb{R}^{n+1}$ spaces is restricted to $n$-dimensional pseudo-spheres. This includes, in particular, the $n$-dimensional de Sitter and Anti-de Sitter space-times. The restriction is designed to extract the corresponding $n$-dimensional Laplace-de Rham operator acting on the corresponding $n$-dimensional one-form on pseudo-spheres. Explicit formulas relating these two operators are given in each situation. The converse problem, of extending an $n$-dimensional operator composed of the sum of the Laplace-de Rham operator and additional terms to ambient spaces Laplace-de Rham operator, is also studied. We show that for any additional term this operator on the embedded space is the restriction of Laplace-de Rham operator on the embedding space.These results are translated to the Laplace-Beltrami operator thanks to the Weitzenböck formula, for which a proof is also given.
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