Whereas differential invariants can involve a distinguished choice of independent variables ( or a parameterization ), geometric invariants do not . �lie Cartan's method of moving frames is a refinement that, while less general than Lie's methods of differential invariants, always yields invariants of the geometrical kind.
12.
Whereas differential invariants can involve a distinguished choice of independent variables ( or a parameterization ), geometric invariants do not . �lie Cartan's method of moving frames is a refinement that, while less general than Lie's methods of differential invariants, always yields invariants of the geometrical kind.
13.
In particular, during the geometrical seminar P . A . Shirokov studied with the staff of department, students and graduate students the general theory of differential invariants generalized spaces that were being developed in those years in the USA by Princeton geometrical school ( L . Eisenhart, O . Veblen, T . Thomas, D . Thomas, J . Whitehead, etc . ).
14.
The area was much studied by mathematicians from around 1890 for a generation ( by J . G . Darboux, George Henri Halphen, Ernest Julius Wilczynski, E . Bompiani, G . Fubini, Eduard & # 268; ech, amongst others ), without a comprehensive theory of differential invariants emerging . �lie Cartan formulated the idea of a general projective connection, as part of his method of moving frames; abstractly speaking, this is the level of generality at which the Erlangen program can be reconciled with differential geometry, while it also develops the oldest part of the theory ( for the projective line ), namely the Schwarzian derivative, the simplest projective differential invariant.
15.
The area was much studied by mathematicians from around 1890 for a generation ( by J . G . Darboux, George Henri Halphen, Ernest Julius Wilczynski, E . Bompiani, G . Fubini, Eduard & # 268; ech, amongst others ), without a comprehensive theory of differential invariants emerging . �lie Cartan formulated the idea of a general projective connection, as part of his method of moving frames; abstractly speaking, this is the level of generality at which the Erlangen program can be reconciled with differential geometry, while it also develops the oldest part of the theory ( for the projective line ), namely the Schwarzian derivative, the simplest projective differential invariant.
