Victor Andreevich Toponogov
Encyclopedia
Victor Andreevich Toponogov was a Russia
n mathematician
, noted for his contributions to differential geometry and so-called Riemannian geometry
"in the large".
After finishing secondary school in 1948, Toponogov entered the department of Mechanics and Mathematics at Tomsk State University
, graduated with honours in 1953, and continued as a graduate student there until 1956. He moved to an institution in Novosibirsk
in 1956 and lived in that city for the rest of his career. Since the institution at Novosibirsk had not yet been fully credentialed, he had defended his Ph.D. thesis at Moscow State University in 1958, on a subject in Riemann spaces. Novosibirsk State University
was established in 1959. In 1961 Toponogov became a professor at a newly created Institute of Mathematics and Computing in Novosibirsk affiliated with the state university.
Toponogov's scientific interests were influenced by his advisor Abram Fet, who taught at Tomsk and later at Novosibirsk. Fet was a well-recognized topologist and specialist in variational calculus in the large. Toponogov's work was also strongly influenced by the work of Aleksandr Danilovich Aleksandrov
. Later, the class of metric space
s known as CAT(k) spaces
would be named after Élie Cartan
, Aleksandrov and Toponogov.
Toponogov published over forty papers and some books during his career. His works are concentrated in Riemannian geometry "in the large". A significant number of his students also made notable contributions in this field.
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, noted for his contributions to differential geometry and so-called Riemannian geometry
Riemannian geometry
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point which varies smoothly from point to point. This gives, in particular, local notions of angle, length...
"in the large".
After finishing secondary school in 1948, Toponogov entered the department of Mechanics and Mathematics at Tomsk State University
Tomsk State University
Tomsk State University , formerly Imperial Tomsk University, is the first university in Siberia—it was founded in 1878 in Tomsk, Russia. TSU opened in 1888 with only one department, the medical school...
, graduated with honours in 1953, and continued as a graduate student there until 1956. He moved to an institution in Novosibirsk
Novosibirsk
Novosibirsk is the third-largest city in Russia, after Moscow and Saint Petersburg, and the largest city of Siberia, with a population of 1,473,737 . It is the administrative center of Novosibirsk Oblast as well as of the Siberian Federal District...
in 1956 and lived in that city for the rest of his career. Since the institution at Novosibirsk had not yet been fully credentialed, he had defended his Ph.D. thesis at Moscow State University in 1958, on a subject in Riemann spaces. Novosibirsk State University
Novosibirsk State University
Novosibirsk State University was founded in May 1959 in the USSR by Soviet academicians Mikhail Alekseevich Lavrentiev, Sergei Lvovich Sobolev and Sergey Alekseyevich Khristianovich in a program of establishing a Siberian branch of the USSR Academy of Sciences...
was established in 1959. In 1961 Toponogov became a professor at a newly created Institute of Mathematics and Computing in Novosibirsk affiliated with the state university.
Toponogov's scientific interests were influenced by his advisor Abram Fet, who taught at Tomsk and later at Novosibirsk. Fet was a well-recognized topologist and specialist in variational calculus in the large. Toponogov's work was also strongly influenced by the work of Aleksandr Danilovich Aleksandrov
Aleksandr Danilovich Aleksandrov
Aleksandr Danilovich Aleksandrov , and Alexandrov ) , was a Soviet/Russian mathematician, physicist, philosopher and mountaineer.- Scientific career :...
. Later, the class of metric space
Metric space
In mathematics, a metric space is a set where a notion of distance between elements of the set is defined.The metric space which most closely corresponds to our intuitive understanding of space is the 3-dimensional Euclidean space...
s known as CAT(k) spaces
CAT(k) space
In mathematics, a CAT space is a specific type of metric space. Intuitively, triangles in a CAT space are "slimmer" than corresponding "model triangles" in a standard space of constant curvature k. In a CAT space, the curvature is bounded from above by k...
would be named after Élie Cartan
Élie Cartan
Élie Joseph Cartan was an influential French mathematician, who did fundamental work in the theory of Lie groups and their geometric applications...
, Aleksandrov and Toponogov.
Toponogov published over forty papers and some books during his career. His works are concentrated in Riemannian geometry "in the large". A significant number of his students also made notable contributions in this field.