2014年6月4日 · Could you recommend a good introductory book(s) or web sites (besides Wikipedia, of which I am aware ) on the subject of the 3-sphere. My goal is to build intuition …

2012年1月9日 · What you have at the top is not the metric of a 3-sphere, but simply the metric of R^3 in spherical polar coordinates. A 3-sphere metric will have r fixed and 3 angles to describe …

2022年3月5日 · A 1-sphere exists in 2D space. It is a circle in flat space. A 2-sphere is a 1-sphere embedded in 3D space. Its surface is non flat and 2 dimensional. A 3-sphere is a 2-sphere …

2014年9月22日 · For the first case involving a 3-sphere embedded in 4D Euclidean space, the line element can be written as follows:##ds^2 = a^2[(d\chi^2)+sin^{2} …

2015年10月28日 · A 3-sphere is a sphere in 4D space. A 3-sphere -- or any other object in 4space with non-zero volume -- can have two planes of rotation. These planes are always at …

2008年1月20日 · I have been trying to figure out the line element on a 3-sphere for my GR class. Problem is that I am trying to go the traditional way of finding dx, dy, dz, and dw, then regroup …

2024年1月22日 · Hi, ##SU(2)## group as topological space is homeomorphic to the 3-sphere ##\\mathbb S^3##. Since ##SU(2)## matrices are unitary there is a natural bijection between …

2017年6月2日 · The ##3-##sphere (with radius ##1##) is a three dimensional analytic manifold. Two possible ways of looking at it are $$\mathbb{S}^3 \simeq U(1,\mathbb{H}) \cong …

2017年10月16日 · Which brings me to my current problem. Now Rovelli is talking about how Einstein’s theory of General Relativity led him to the conclusion that the universe is a 3 …

2020年11月28日 · In the case of the 3 sphere its equator is a regular two dimensional sphere and the two pieces are ordinary solid balls. In 4 space these balls are puffed up into the fourth …