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On Simple Families of Functions and Their Legendrian Mappings
Author(s) -
Garay Mauricio D.
Publication year - 2004
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611503014370
Subject(s) - mathematics , simple (philosophy) , pure mathematics , equivalence (formal languages) , parameter space , diagram , mathematics subject classification , degeneracy (biology) , space (punctuation) , combinatorics , geometry , statistics , bioinformatics , philosophy , epistemology , biology , linguistics
We study germs of n ‐parameter families of functions, that is, function‐germs of the type f : R n × R, 0) → R , 0 defined on the total space of the trivial bundle R n × R → R n . There is a natural notion of V ‐equivalence for such function‐germs. We introduce the Young diagram of n ‐parameter families satisfying a non‐degeneracy condition. We classify all such simple n ‐parameter families and give their versal deformations. This result has direct applications to contact and projective geometry. 2000 Mathematics Subject Classification 37G25, 14N15.