# How do we understand and visualize the meridians of a 3-sphere?

The equator of a n-sphere is (n-1)-sphere. Then the equator of a 3-sphere is a 2-sphere. Does this mean the meridian of a 3-sphere is a hemisphere (half 2-sphere)? In contrast, Wikipedia describes the meridians as 1-dimensional curves here: http://en.wikipedia.org/wiki/3-sphere

Also, how does one visualize the meridians of the 3-sphere? Naturally, this will involve stereographic projection, but it will be very good to see details and images (videos would be great!).

Is there a good book one can have that deals in good details with the meridians of the 3-sphere?

Many thanks.

• This is interesting. I don't quite know the answer, but does the 3-sphere even have poles? – PA6OTA May 1 '14 at 14:43
• It's not obvious what is meant by a "meridian" on a $3$-sphere. A meridian on a $2$-sphere has dimension $1$ and codimension $1$. Which of the two should be generalized? Depending on the answer your "meridian" is part of a circle or part of a $2$-sphere. – Christian Blatter May 1 '14 at 18:45
• the $S^3$ allows a foliation with 2-tori being a Hopf's link the bidding. – janmarqz May 2 '14 at 20:46
• People say the 3-sphere is well studied. I would like to read more about this, specifically about its meridians... This link gives only a very good initial thoughts: theory.org/geotopo/3-sphere/html – Jay May 4 '14 at 16:38
• @janmarqz: do you mean that “poles” are two circles and S¹ × S¹ foils fill the S³ in between? (if I remember correctly, it’s called a join).  Jay: insufficient context. What is your motivation to define meridians on S³ as surfaces? I haven’t a problem to imagine S³; I have a problem to understand what are you speaking about. – Incnis Mrsi Nov 11 '14 at 20:33