论文标题
laplace操作员对单色的限制：从$ \ mathbb {r}^{n+2} $和$ \ mathbb {r}^{n+1} $环境空间embedded（a）ds $ _n $ submanifolds
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
论文作者
论文摘要
在$ \ Mathbb {r}^{n+2} $或$ \ Mathbb {r}^{r}^{n+1} $ space限制为$ n $ n $ dimemensional-dimemensional-dimemensional-demensional-depspheres。这尤其包括$ n $维的de保姆和反de保姆空间时间。该限制旨在提取相应的$ n $维laplace-de rham操作员，该操作员作用于相应的$ n $二维一式伪造的伪型。在每种情况下都给出了与这两个操作员有关的明确公式。还研究了将$ n $维操作员扩展的问题，该操作员由Laplace-DE RHAM操作员的总和和其他条款组成，并将其其他条款延伸到环境空间Laplace-de Rham操作员。我们表明，对于任何其他术语，该操作员在嵌入式空间上的限制是在嵌入空间上限制Laplace-DE RHAM操作员。由于Weitzenböck公式，这些结果被转化为Laplace-Beltrami操作员，也给出了证明。
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.
