数学上，如以前星空兄所说，必须需要至少七维时空才能容纳任意一个三维的物体。
那么，我们的宇宙里可能存在这样的物体吗？如果它确实存在，那么，当人们遇到它，探测它的时候，会得到什么样的奇妙结果？

抱歉，记错了！
是萍踪兄的帖子里提到的。
http://www.changhai.org/forum/article_load.php?fid=5&aid=1175888776

如果是三维流形,我记得六维欧氏空间应该够了.但是这样的嵌入比较特殊,
在七维欧氏中这样的嵌入是一般的.

必须要有7维才可以无自交点地嵌入，而且还只是拓扑意义的嵌入。要在微分几何意义上嵌入，要用到Nash嵌入定理，对外围空间的维数要求要高得多

最简单的RP^3不能放入R^4.

我好像记得，著名的Klein瓶就是一个本质上是3维的流形，但是，它又不可能在三维平直空间里出现，只有4维及以上空间才能够容纳它？
对否？

我查到资料，严格的说，Klein瓶是一个二维的曲面。我这里指的是它包围的封闭空间是三维的。

2维Poincare上半平面也不能嵌入R^4，那么只要构造其与R的直积就可以知道也必然无法嵌入R^4

从Wiki百科查的。
http://en.wikipedia.org/wiki/Hassler_Whitney

In a 1936 paper, Whitney gave a definition of a "smooth manifold of class Cr", and proved that, for high enough values of r, a smooth manifold of dimension n may be embedded in R^2n+1, and immersed in R^2n. (In 1944 he managed to reduce the dimension of the ambient space by 1, so long as n > 2, by a technique that has come to be known as the "Whitney trick.") This basic result shows that manifolds may be treated intrinsically or extrinsically, as we wish.

In mathematics, particularly in differential topology,there are two Whitney embedding theorems:

The strong Whitney embedding theorem states that any connected smooth m-dimensional manifold (required also to be Hausdorff and second-countable) can be smoothly embedded in Euclidean 2m-space. This is the best linear bound on the smallest-dimensional Euclidean space that all m-dimensional manifolds embed in, as the real projective spaces of even dimension m cannot be embedded into Euclidean (2m − 1)-space (as can be seen from a characteristic class argument, also due to Whitney).

The weak Whitney embedding theorem states that any continuous function from an n-dimensional manifold to an m-dimensional manifold may be approximated by a smooth embedding provided m>2n. Whitney similarly proved that such a map could be approximated by an immersion provided m>2n-1. This last result is sometimes called the weak Whitney immersion theorem.

http://en.wikipedia.org/wiki/Whitney_embedding_theorem 上给出了证明思路。

有一个电影《超级立方体2》很像类似的情景 我一直都保存着