M-theory backgrounds in the form of unwarped compactifications with or without fluxes are considered. We construct the bilinear forms of supergravity Killing spinors for different choices of spinor inner products on these backgrounds. The equations satisfied by the bilinear forms and their decompositions into product manifolds are obtained for different inner product choices in the special case for which the spinors factorize. It is found that the AdS solutions can only appear for some special choices of spinor inner products on product manifolds. The reduction of bilinears of supergravity Killing spinors into the hidden symmetries of product manifolds which are Killing-Yano and closed conformal Killing-Yano forms for AdS solutions is shown. These hidden symmetries are lifted to eleven-dimensional backgrounds to find the hidden symmetires on them. The relation between the choices of spinor inner products, AdS solutions and hidden symmetries on M-theory backgrounds are investigated.

考虑具有或不具有通量的无翘曲压实形式的M理论背景。在这些背景下，我们针对不同的转子内部产品选择构建了超线性Killing转子的双线性形式。在特殊情况下，由于旋转子分解，双线性形式满足的方程及其分解为产品流形获得了不同的内部产品选择。发现AdS解决方案只能出现在产品歧管上某些特殊的旋转内衬产品中。将超重力Killing旋子的双线性减少为产品流形的隐藏对称形式，即AdS的Killing-Yano和闭合保形Killing-Yano形式显示了解决方案。将这些隐藏的对称性提升到11维背景，以在其上找到隐藏的对称性。研究了M理论背景下的内转子选择，AdS解和隐式对称性之间的关系。