Abelian categoryIn mathematics, an abelian category is a in which morphisms and can be added and in which s and cokernels exist and have desirable properties. The motivating prototypical example of an abelian category is the , Ab. The theory originated in an effort to unify several cohomology theories by Alexander Grothendieck and independently in the slightly earlier work of David Buchsbaum. Abelian categories are very stable categories; for example they are and they satisfy the snake lemma.
Causes of the Great DepressionThe causes of the Great Depression in the early 20th century in the United States have been extensively discussed by economists and remain a matter of active debate. They are part of the larger debate about economic crises and recessions. The specific economic events that took place during the Great Depression are well established. There was an initial stock market crash that triggered a "panic sell-off" of assets.
Kähler manifoldIn mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure. The concept was first studied by Jan Arnoldus Schouten and David van Dantzig in 1930, and then introduced by Erich Kähler in 1933. The terminology has been fixed by André Weil.
Great DepressionThe Great Depression (19291939) was an economic shock that impacted most countries across the world. It was a period of economic depression that became evident after a major fall in stock prices in the United States. The economic contagion began around September 1929 and led to the Wall Street stock market crash of October 24 (Black Thursday). It was the longest, deepest, and most widespread depression of the 20th century. Between 1929 and 1932, worldwide gross domestic product (GDP) fell by an estimated 15%.
Scalar curvatureIn the mathematical field of Riemannian geometry, the scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the geometry of the metric near that point. It is defined by a complicated explicit formula in terms of partial derivatives of the metric components, although it is also characterized by the volume of infinitesimally small geodesic balls.
