Fiber normal

In differential Geometry, a normal fiber is a particular kind of Fibré vectorial.

Definition

That is to say (M, G) a Variety riemannienne, and $S \ subset M$ a subvariety riemannienne.

One defines, for $p \ in fixed S$, a vector $n \ in \ mathrm \left\{T\right\} _p orthogonal M$ with $\ mathrm \left\{T\right\} _p S$, i.e. normal with any vector $v \ in \ mathrm \left\{T\right\} _p S$, that is to say still $g \left(N, v\right) =0$ for each one of these vectors v .

The unit $\ mathrm \left\{NR\right\} _p S$ of these vectors $n$ is called normal space with $S$ in $p$.

Just as the total space of the tangent Fibré with a variety is built from all the tangent spaces with the variety, the total space of fiber normal $\ mathrm \left\{NR\right\} S$ with $S$ is defined by:

$\ mathrm \left\{NR\right\} S: = \ coprod_ \left\{p \ in S\right\} \ mathrm \left\{NR\right\} _p S$.

Fiber conormal

The fiber conormal is defined like the normal Fibré dual of fiber. It is a under-fiber of the Fibré cotangent.

References

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