X-Nico

unusual facts about Hopf-Rinow theorem



Clifton–Pohl torus

While every compact Riemannian manifold is also geodesically complete (by the Hopf–Rinow theorem), this space shows that the same implication does not generalize to pseudo-Riemannian manifolds.

Commentarii Mathematici Helvetici

In 1931 Hans Hopf and his student Rinow published the Hopf-Rinow theorem in their article "Über den Begriff der vollständigen differentialgeometrischen Fläche".

Dirk Kreimer

Dirk Kreimer (born 1960) is a German physicist who pioneered the Hopf-algebraic approach to quantum field theory with Alain Connes and other co-authors.

Evolution of sexual reproduction

Several explanations have been suggested by biologists including W. D. Hamilton, Alexey Kondrashov, George C. Williams, Harris Bernstein, Carol Bernstein, Michael M. Cox, Frederic A. Hopf and Richard E. Michod to explain how sexual reproduction is maintained in a vast array of different living organisms.

Hopf bifurcation

In the mathematical theory of bifurcations, a Hopf or Poincaré–Andronov–Hopf bifurcation, named after Henri Poincaré, Eberhard Hopf, and Aleksandr Andronov, is a local bifurcation in which a fixed point of a dynamical system loses stability as a pair of complex conjugate eigenvalues of the linearization around the fixed point cross the imaginary axis of the complex plane.

Karl Hopf

Karl Hopf (Hamm, Westphalia, February 19, 1832 – Wiesbaden, August 23, 1873) or Carl Hermann Friedrich Johann Hopf was historian and expert in Medieval Greece, both Byzantine and Frankish.


see also