Hidehiko Yamabe

Hidehiko Yamabe
Born(1923-08-22)August 22, 1923
Ashiya, Hyōgo
DiedNovember 20, 1960(1960-11-20) (aged 37)
Evanston, Illinois
NationalityJapanese
Alma materUniversity of Tokyo
Known forHilbert's fifth problem, Yamabe flow, Yamabe invariant, Yamabe problem
Scientific career
FieldsDifferential geometry, Group theory
InstitutionsOsaka University, Princeton University, University of Minnesota, Northwestern University
Doctoral advisorShokichi Iyanaga[1]

Hidehiko Yamabe (山辺 英彦, Yamabe Hidehiko, August 22, 1923, in Ashiya, Hyōgo, Japan – November 20, 1960, in Evanston, Illinois) was a Japanese mathematician. Above all, he is famous for discovering[2] that every conformal class on a smooth compact manifold is represented by a Riemannian metric of constant scalar curvature. Other notable contributions include his definitive solution of Hilbert's fifth problem.[3]

  1. ^ According to the Yamabe Symposium Organizing Committee (2008, p. 6)
  2. ^ Lee and Parker, The Yamabe Problem, Bull. Amer. Math. Soc. (N.S.) 17 (1987), no. 1, 37–91.
  3. ^ According to Goto (1961, p. i): however, the question is still debated since in the literature there have been other such claims, largely based on different interpretations of Hilbert's statement of the problem given by various researchers. For a review of recent claims (however completely ignoring the contributions of Yamabe) and for a new one, see Rosinger (1998, pp. xiii–xiv and pp. 169–170). For a general review, including an historical sketch dealing with all contributors, see the Hilbert's fifth problem entry.