Noboru Tanaka (mathematician)

from Wikipedia, the free encyclopedia

Noboru Tanaka ( Japanese 田中 昇 , Tanaka Noboru ; born April 11, 1930 in Iida , Nagano prefecture ) is a Japanese mathematician who dealt with (complex) differential geometry and Lie groups, often starting from the work of Élie Cartan .

Life

Tanaka studied mathematics at Nagoya University in the 1950s with the differential geometry meters Y. Matsushima , K. Nomizu and M. Kuranishi .

Tanaka developed the differential geometric methods (Cartan relationships) introduced by Élie Cartan for the study of Henri Poincaré's problem (1907) on the question of the local pseudo-conformal equivalence of real hypersurfaces in complex spaces. He succeeded in solving the equivalence problem of nondegenerate real hypersurfaces in n-dimensional complex spaces (treated by Élie Cartan for n = 2). He dealt with a special case in 1962, announced the general solution in 1965 and published the details in 1976 as part of a more general theory of Cartan relationships he developed. His methods were fundamental to the development of conformal geometry and especially CR structures.

From 1965 he was a professor at the University of Kyoto . Here he continued his investigations into geometric equivalence problems. Among other things, he developed Cartan relationships for geometric structures connected with simple, graded Lie algebras. He also dealt with analytical problems (global analysis) and geometric theory of (ordinary) differential equations.

In 1978 he became a professor at the University of Hokkaidō .

Fonts

  • On the pseudo-conformal geometry of hypersurfaces of the space of n complex variables, J. Math. Soc. Japan, Vol. 14, 1962, pp. 397-429
  • Graded Lie algebras and geometric structures, Proc. US-Japan Seminar in Differential Geometry, Kyoto 1965, Nippon Hyoronsha, Tokyo 1966, pp. 147-150
  • On generalized graded Lie algebras and geometric structures. I, J. Math. Soc. Japan, Volume 19, 1967, pp. 215-254
  • On differential systems, graded Lie algebras and pseudogroups, J. Math. Kyoto Univ., Volume 10, 1970, pp. 1-82
  • On non-degenerate real hypersurfaces, graded Lie algebras, and Carton connections, Japan J. Math., Volume 2, 1976, pp. 131-190
  • A differential geometric study on strongly pseudo-convex manifolds, Tokyo 1975

literature

  • Vladimir Ezhov, Ben McLaughlin, Gerd Schmalz From Cartan to Tanaka: getting real in the complex world , Notices AMS, Volume 58, January 2011 (with photo), Online

Web links

Individual evidence

  1. ↑ 田中 昇 . researach-er.jp, accessed January 7, 2015 (Japanese).
  2. ↑ Raymond Wells, The Cauchy-Riemann equations and Differential Geometry, Bulletin AMS, Volume 6, 1982, p. 187, pdf
personal data
SURNAME Tanaka, Noboru
ALTERNATIVE NAMES 田中 昇 (Japanese)
BRIEF DESCRIPTION Japanese mathematician
DATE OF BIRTH April 11, 1930
PLACE OF BIRTH Iida