- 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"...
-
Undergraduate Texts in Mathematics, Springer-Verlag, ISBN 0387903577
Toponogov,
Victor A. (2005),
Differential Geometry of
Curves and Surfaces: A Concise...
-
inequality Ptolemy's
inequality Pu's
inequality Riemannian Penrose inequality Toponogov's theorem Triangle inequality Weitzenböck's
inequality Wirtinger inequality...
-
comparison theorem Morse index theorem Synge theorem Weinstein theorem Toponogov theorem Sphere theorem Hodge theory Uniformization theorem Yamabe problem...
- of the
sectional curvatures by λ − 1 . {\displaystyle \lambda ^{-1}.}
Toponogov's theorem affords a
characterization of
sectional curvature in
terms of...
- > 0 {\displaystyle \lambda >0} is a
positive constant.
Darboux frame Toponogov (2006) This
equation is the
basis for Gauss's
theorema egregium. Gauss...
