Math @ Duke

Publications [#318280] of Robert Bryant
search www.ams.org.Papers Published
 Bryant, R, On notions of equivalence of variational problems with one independent variable,
in Differential geometry: the interface between pure and applied mathematics (San Antonio, Tex., 1986), Contemporary Mathematics, edited by Luksic, M; Martin, C; Shadwick, W, vol. 68
(1987),
pp. 6576, American Mathematical Society, ISBN 082185075X [MR89f:58037]
(last updated on 2019/08/20)
Author's Comments: This is a short expository paper discussing the different
notions
of equivalence, such as simple equivalence, contact
equivalence, and divergence
equivalence for variational problems with one
independent variable. I show
that the group of symmetries under one notion of
equivalence can be distinct
from the group of symmetries under another notion. I
discuss how one can
set up the equivalence problem to compute these
different groups of symmetries,
but do not enter into any actual equivalence
calculations.
Please note: This paper was typeset directly from
my handwritten manuscript
(nearly the last handwritten one I ever produced) and I
did not get to
proofread the result before it appeared. Consequently,
there are many typos,
particularly in the matrices on the last pages.


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