History of The Sphere Theorem
Hopf conjectured that a simply connected manifold with pinched sectional curvature is a sphere. In 1951, Harry Rauch showed that a simply connected manifold with curvature in is homeomorphic to a sphere. In 1960, Berger and Klingenberg proved the topological version of the sphere theorem with the optimal pinching constant.
Read more about this topic: Sphere Theorem
Famous quotes containing the words history of, history, sphere and/or theorem:
“When the history of guilt is written, parents who refuse their children money will be right up there in the Top Ten.”
—Erma Brombeck (20th century)
“The disadvantage of men not knowing the past is that they do not know the present. History is a hill or high point of vantage, from which alone men see the town in which they live or the age in which they are living.”
—Gilbert Keith Chesterton (1874–1936)
“Prayer is the fair and radiant daughter of all the human virtues, the arch connecting heaven and earth, the sweet companion that is alike the lion and the dove; and prayer will give you the key of heaven. As pure and as bold as innocence, as strong as all things are that are entire and single, this fair and invincible queen rests on the material world; she has taken possession of it; for, like the sun, she casts about it a sphere of light.”
—Honoré De Balzac (1799–1850)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)