标题： 感应物质：嵌入在黎曼平坦的N+1维空间中的弯曲N流形 显示英文标题

标题： Induced matter: Curved N-manifolds encapsulated in Riemann-flat N+1 dimensional space

摘要： 利科和韦森最近引入了爱因斯坦方程的一个新的五维诱导物质解，这是一个负曲率的罗伯逊-沃尔克空间，嵌入在一个黎曼平直的五维流形中。 我们表明这个解是更一般的定理的一个特例，该定理规定了某些N+1维黎曼平直空间的结构，这些空间都是爱因斯坦方程的解。 这些解包含了N维弯曲流形。 这样的空间仅凭其几何结构就被称作在子流形中“诱导物质”。 我们证明N维流形可以是任何最大对称空间。 显示英文摘要

摘要： Liko and Wesson have recently introduced a new 5-dimensional induced matter solution of the Einstein equations, a negative curvature Robertson-Walker space embedded in a Riemann flat 5-dimensional manifold. We show that this solution is a special case of a more general theorem prescribing the structure of certain N+1-dimensional Riemann flat spaces which are all solutions of the Einstein equations. These solutions encapsulate N-dimensional curved manifolds. Such spaces are said to "induce matter" in the sub-manifolds by virtue of their geometric structure alone. We prove that the N-manifold can be any maximally symmetric space.