method of moving frames造句

In fact, in the method of moving frames, one more often works with coframes rather than frames.
They have many applications in geometry and physics : see the method of moving frames, Cartan connection applications and Einstein Cartan theory for some examples.
The "'method of moving frames "'of 蒷ie Cartan is based on taking a moving frame that is adapted to the particular problem being studied.
Historically, connection forms were introduced by 蒷ie Cartan in the first half of the 20th century as part of, and one of the principal motivations for, his method of moving frames.
The theory of Cartan connections was developed by 蒷ie Cartan, as part of ( and a way of formulating ) his method of moving frames ( "'rep鑢e mobile "').
It's difficult to find method of moving frames in a sentence. 用method of moving frames造句挺难的

Whereas differential invariants can involve a distinguished choice of independent variables ( or a parameterization ), geometric invariants do not . 蒷ie 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.
The strategy in Cartan's "'method of moving frames "', as outlined briefly in Cartan's equivalence method, is to find a " natural moving frame " on the manifold and then to take its Darboux derivative, in other words pullback the Maurer-Cartan form of " G " to " M " ( or " P " ), and thus obtain a complete set of structural invariants for the manifold.
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 . 蒷ie 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.