Chuan-Chih Hsiung

Chuan-Chi Hsiung , often cited by CC Hsiung, (born February 15, 1915 in Shefong near Nanchang , China , † May 6, 2009 in Needham (Massachusetts) ) was a Sino-American mathematician who studied differential geometry and geometry .

Hsiung came from a farming family, although his grandfather, who died relatively early, trained as a Confucian scholar and his father trained as a mathematics teacher. Hsiang was the third of four sons. The second oldest son, CY Hsiung, also became a math professor. Hsiung studied mathematics from his father and at the high school in Nanchang (10 miles from his hometown). He then studied mathematics at the National Chekiang University in Hangchow , graduating in 1936, where he was a student of Buchin Su. His first publication in 1937 was on projective geometry of space curves. These and other publications attracted the attention of Guy Grove (Vernon Grove) of Michigan State University , who invited him to the United States for a doctorate. This was prevented by the outbreak of war with Japan in 1937. It was not until 1946 that he was able to travel to Grove at Michigan State University, where he received his doctorate in 1948 (Rectilinear Congruences). Until 1950 he was an instructor at Michigan State and then visiting professor at Northwestern University and from 1951 research assistant to Hassler Whitney at Harvard University . In 1952, when Whitney went to the Institute for Advanced Study, Hsiung became Assistant Professor at Lehigh University , where he became Associate Professor in 1955 and Professor in 1960. In 1984 he retired.

At first he dealt with projective differential geometry and projective geometry. In 1942 he proved a sentence about tangram with Fu Traing Wang . They proved that no more than 13 different convex figures could be formed. After his time at Whitney, he turned to global issues in differential geometry. So he dealt with the still open problem of the existence of complex structures . According to Armand Borel and Jean-Pierre Serre (1953), only the spheres in two and six dimensions can carry almost complex structures ; the case of two dimensions is the classic case of the Riemann number sphere as a complex projective space, but in six dimensions there are very many almost complex structures Structures that are mostly non-integrable and therefore do not lead to a complex structure. It is mostly assumed that there are no complex structures on . Hsiung published an attempt to prove it in 1986, but it was flawed. Attempts at proof by Allan Adler (1969) and by SS Chern in 2004, who used the exceptional Lie group and Eichfeld theory techniques, were also incomplete. In addition to complex and almost complex structures, he also investigated isospectal manifolds, conformal transformations of compact Riemann surfaces, isoperimetric inequalities on two-dimensional Riemann manifolds with boundaries and the relationship between curvature and characteristic classes. ${\displaystyle S^{6}}$ ${\displaystyle S^{6}}$ ${\displaystyle G_{2}}$

In 1967 he founded the Journal of Differential Geometry and was editor and later co-editor until his death.

Fonts

• Selected Papers of Chuan-Chih Hsiung, World Scientific 2001
• Almost complex and complex structures, World Scientific 1995
• A first course in differential geometry, 1981, 1997, International Press 2013

Web links

• John J. O'Connor, Edmund F. Robertson :  Chuan-Chih Hsiung. In: MacTutor History of Mathematics archive .

Individual evidence

1. ↑ Borel, Serre, Groupes de Lie et et puissantes réduites de Steenrod, American Journal of Mathematics, Volume 75, 1953, pp. 409-448.
2. ^ Hsiung, Non-existence of a complex structure on the six-sphere, Bull. Inst. Math. Acad. Sinica, Vol. 14, 1986, pp. 231-247.
3. ↑ Robert Bryant , SS Chern's study of complex structures on the six sphere, 2014 Arxiv
4. ↑ See introduction to Gabor Etesi, The six-dimensional sphere is a complex manifold , Arxiv 2015 , he claims to have found a complex structure in it, a preprint by Michael Atiyah from 2016 claims to have proven the non-existence