I was thinking about a research topic, and I had was wondering- how might one extend the 3 dimensional plane to 4 dimensions? I know that for a 2 dimensional plane we can extend it to a 3 dimensional Riemann Sphere? Perhaps you could point me in the general direction? What would the name of such a object be? What is the general method of extending planes in such a way that, in the case of Riemann Sphere, positive infinity equals negative infinity?
Many thanks,
Amadeus
I am sorry. I know this is a bogus answer. Perhaps, given one has a three dimensional plane (or perhaps we could call it a hyperplane), one interpretation is to regard this slice of time as being the static hyperplane we have drawn. A common way I introduce a fourth dimension is to turn on time, so we have a dynamical system perhaps whose image is a hyperplane residing in (R^3)XR. I realize this is banal, and can't blame you if you mark me down.