Let 
be a nilpotent,
connected, simply connected Lie
group, and let 
be a discrete subgroup of 
with compact right quotient
space. Then 
is called a nilmanifold.
Nilmanifold
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Cite this as:
Weisstein, Eric W. "Nilmanifold." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Nilmanifold.html