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668: １３２人目の素数さん [] 2023/03/22(水) 16:10:22.80 ID:VqclUbtx

>>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)

http://rio2016.5ch.net/test/read.cgi/math/1677671318/668

669: １３２人目の素数さん [] 2023/03/22(水) 16:55:01.38 ID:VqclUbtx

>>668
>Levi-Tanaka Algebra and Tanaka’s Prolongation Procedure

下記か？
https://www.researchgate.net/publication/225316341_Classification_of_semisimple_Levi-Tanaka_algebras
Article PDF Available
Classification of semisimple Levi-Tanaka algebras
January 1998Annali di Matematica Pura ed Applicata 174(1):285-349
Authors:
Costantino Medori
Universita di Parma
Mauro Nacinovich
University of Rome Tor Vergata

https://en.wikipedia.org/wiki/L%C3%A9vy_process
Levy process
In probability theory, a Levy process, named after the French mathematician Paul Levy, is a stochastic process with independent, stationary increments: it represents the motion of a point whose successive displacements are random, in which displacements in pairwise disjoint time intervals are independent, and displacements in different time intervals of the same length have identical probability distributions. A Levy process may thus be viewed as the continuous-time analog of a random walk.

https://en.wikipedia.org/wiki/Paul_L%C3%A9vy_(mathematician)
Paul Pierre Levy (15 September 1886 ? 15 December 1971)[2] was a French mathematician who was active especially in probability theory, introducing fundamental concepts such as local time, stable distributions and characteristic functions.

https://en.wikipedia.org/wiki/Tanaka%27s_formula
Tanaka's formula
https://en.wikipedia.org/wiki/Tanaka_equation
Tanaka equation

https://en.wikipedia.org/wiki/Local_time_(mathematics)
Local time (mathematics)
Local time appears in various stochastic integration formulas, such as Tanaka's formula, if the integrand is not sufficiently smooth. It is also studied in statistical mechanics in the context of random fields.
Tanaka's formula

http://rio2016.5ch.net/test/read.cgi/math/1677671318/669

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