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1
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40
on Cartan´s method of Lie groups and moving frames as applied to uniqueness and existence.pdf
P. Griffiths
"on Cartan´s method of Lie groups and moving frames as applied to uniqueness and existence"

These notes re n exposition of the philosophy due to ESe Crtn that, v
the use of moving frames, the theory of Lie groups constitutes powerful nd
elegant method for studying uniqueness nd existence questions for submnifolds
of homogeneous spce. This philosophy, as expounded in his beautiful book
"Groupes finis et continus et l gomtrie diffrentielle", Gauthier-Villrs
(Pris), is perhaps not s widely appreciated s it should be, especially s
regards the higher order inwrints of submnifold. A possible reson for
this is that, even though the bsic Lie group statements underlying the theory
re of rther general nture, their ppliction to geometry seems t present
more dpted to special cases depending on subtle conditions of non-degeneracy,
rather thn constituting vast general theory. It is the intricacy nd beauty
of these special cses which in the end justifies
168
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68
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