- the
mathematical field of
Riemannian geometry,
Toponogov's theorem (named
after Victor Andreevich Toponogov) is a
triangle comparison theorem. It is one...
-
Victor Andreevich Toponogov (Russian: Ви́ктор Андре́евич Топоно́гов;
March 6, 1930 –
November 21, 2004) was an
outstanding Russian mathematician, noted...
- Cartan,
Aleksandr Danilovich Aleksandrov and
Victor Andreevich Toponogov (although
Toponogov never explored curvature bounded above in publications). For...
-
proved the
theorem in the case of two-dimensional manifolds, and
Victor Toponogov had
extended Cohn-Vossen's work to
higher dimensions,
under the special...
- doi:10.1007/s11511-008-0022-7, S2CID 15463483
Riemannian geometry by V. A.
Toponogov at the
Encyclopedia of
Mathematics Weisstein, Eric W., "Riemannian Geometry"...
- of the
sectional curvatures by λ − 1 . {\displaystyle \lambda ^{-1}.}
Toponogov's theorem affords a
characterization of
sectional curvature in
terms of...
- S2CID 119659239. Guilfoyle, B.; Klingenberg, W. (2024). "Proof of the
Toponogov Conjecture on
complete surfaces". J. Gökova Geom. Topol. GGT. 17: 1–50...
- > 0 {\displaystyle \lambda >0} is a
positive constant.
Darboux frame Toponogov (2006) This
equation is the
basis for Gauss's
theorema egregium. Gauss...
- vol. 5, Providence,
Rhode Island:
American Mathematical Society, p. 3
Toponogov,
Victor A. (2006), "1.5 Problems:
convex plane curves", in Rovenski, Vladimir...
- S2CID 119659239. Guilfoyle, B.; Klingenberg, W. (2024). "Proof of the
Toponogov Conjecture on
complete surfaces". J. Gökova Geom. Topol. GGT. 17: 1–50...
