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

The unit $\ mathrm {NR} _p S$ 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 $\ mathrm {NR} S$ with $S$ is defined by:

\ mathrm {NR} S: = \ coprod_ {p \ in S} \ mathrm {NR} _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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