23/03/22 16:10:22.80 VqclUbtx.net
>>667
つづき
In order to solve this equivalence problem
for real hypersurfaces in C2
, Elie Cartan [6], [7]
constructed in 1932 a “hyperspherical connection” by applying his method of moving frames.
The technique of Cartan has been further developed by introducing modern geometric and
algebraic tools, mainly in the groundbreaking
work by Noboru Tanaka (see [22], [23], [24]).
These powerful and elegant methods are widely
used in conformal geometry and have led to the
development of parabolic geometry (see [5]), while
Cartan’s original approach, applied to hypersurfaces in higher dimensional complex space by
Shiing-Shen Chern and Jurgen Moser [8], is still
dominant in complex analysis (see, e.g., [12], [13]).
Finally, according to Tanaka’s results, the choice
of the Cartan connection is controlled by the
∂-exact components of the curvature.
P24
Levi-Tanaka Algebra and Tanaka’s Prolongation Procedure
略
(引用終り)