The normal bundle of a submanifold 
is the vector bundle
over 
that consists of all pairs 
, where 
is in 
and 
is a vector in the vector quotient space 
. Provided 
has a Riemann metric, 
can be thought of as the orthogonal complement to 
.
Normal Bundle
This entry contributed by Ryan Budney
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Budney, Ryan. "Normal Bundle." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/NormalBundle.html