Viktor Andreevich Toponogov

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Toponogow

Viktor Andreevich Toponogov , Russian Ви́ктор Андре́евич Топоно́гов , English transcription Victor Andreevich Toponogov , (born March 6, 1930 in Tomsk ; † November 21, 2004 in Novosibirsk ) was a Russian mathematician who dealt with differential geometry ( Riemannian geometry ).

Life

Toponogow studied mathematics at Tomsk State University with a degree in 1953. His career was hampered by the fact that his father was considered an enemy of the people and fell victim to the Stalinist terror . That improved somewhat after Stalin's death in 1953. After graduating, Toponogow went to Novosibirsk to the Institute for Radiophysics and Electronics of Yuri Borissowitsch Rumer and received his doctorate in 1958 at Lomonosov University under Abram Ilyich Fet . In 1961 he went to the newly founded Institute of Mathematics of the Siberian Branch of the Soviet Academy of Sciences in Novosibirsk. In 1968 he completed his habilitation ( Russian doctorate ) with the dissertation Extreme Problems for Riemannian Spaces with Curvature Limited from Above . From 1980 to 1982 he was Vice Director of the Institute for Mathematics and from 1982 to 2000 laboratory manager at the institute. In 2001 he became a senior scientist in the Analysis and Geometry Department.

Toponogow was influenced by Fet (who was a student of Lasar Aronowitsch Ljusternik and dealt with differential geometry on a large scale, topology and the calculus of variations) and the geometer Alexander Danilowitsch Alexandrow , who brought synthetic methods in differential geometry back to the fore.

The toponogov's theorem from his doctorate from 1958 makes a statement about the comparison geodetic triangles at a point as a function of a lower bound for the curvature (it is based on work by Alexandrov). It was the starting point for further research on the relationship between the properties of geodesics, curvature and topology.

Later he dealt with the embedding of two-dimensional surfaces in three-dimensional Euclidean space.

He was invited speaker at the International Congress of Mathematicians in Moscow in 1966.

CAT (k) rooms were named in 1987 by Mikhail Leonidowitsch Gromow after Elie Cartan , Alexander Danilowitsch Alexandrow and Toponogow.

Fonts

  • Differential geometry of curves and surfaces. A concise guide, Birkhäuser 2006

Web links

personal data
SURNAME Toponogow, Viktor Andreevich
ALTERNATIVE NAMES Toponogov, Victor Andreevich (English transcription); Топоно́гов, Ви́ктор Андре́евич (Russian)
BRIEF DESCRIPTION Russian mathematician
DATE OF BIRTH March 6, 1930
PLACE OF BIRTH Tomsk
DATE OF DEATH November 21, 2004
Place of death Novosibirsk