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Difference between revisions of "Fold"

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====References====
 
====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> L.V. Hörmander,   "The analysis of linear partial differential operators" , '''3''' , Springer (1985)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> V.I. Arnol'd,   S.M. [S.M. Khusein-Zade] Gusein-Zade,   A.N. Varchenko,   "Singularities of differentiable maps" , '''1''' , Birkhäuser (1985) (Translated from Russian)</TD></TR></table>
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<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> L.V. Hörmander, "The analysis of linear partial differential operators" , '''3''' , Springer (1985) {{MR|1540773}} {{MR|0781537}} {{MR|0781536}} {{ZBL|0612.35001}} {{ZBL|0601.35001}} </TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> V.I. Arnol'd, S.M. [S.M. Khusein-Zade] Gusein-Zade, A.N. Varchenko, "Singularities of differentiable maps" , '''1''' , Birkhäuser (1985) (Translated from Russian) {{MR|777682}} {{ZBL|0554.58001}} </TD></TR></table>

Revision as of 16:57, 15 April 2012

A type of singularity of differentiable mappings (cf. Singularities of differentiable mappings).

Let be a -function. Then is said to be a fold of if

and if the Hessian of at is not equal to zero (cf. Hessian of a function). This definition can be generalized to the case of a -mapping between -manifolds and (necessarily of the same dimension), cf. [a1].

The name derives from the following fact: If (with , and as above) has a fold at , then there are local coordinates in vanishing at and local coordinates in vanishing at such that has the local representation

References

[a1] L.V. Hörmander, "The analysis of linear partial differential operators" , 3 , Springer (1985) MR1540773 MR0781537 MR0781536 Zbl 0612.35001 Zbl 0601.35001
[a2] V.I. Arnol'd, S.M. [S.M. Khusein-Zade] Gusein-Zade, A.N. Varchenko, "Singularities of differentiable maps" , 1 , Birkhäuser (1985) (Translated from Russian) MR777682 Zbl 0554.58001
How to Cite This Entry:
Fold. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fold&oldid=24441