Formal Definition
Hyperbolic n-space, denoted Hn, is the maximally symmetric, simply connected, n-dimensional Riemannian manifold with constant sectional curvature −1. Hyperbolic space is the principal example of a space exhibiting hyperbolic geometry. It can be thought of as the negative-curvature analogue of the n-sphere. Although hyperbolic space Hn is diffeomorphic to Rn its negative-curvature metric gives it very different geometric properties.
Hyperbolic 2-space, H², is also called the hyperbolic plane.
Read more about this topic: Hyperbolic Space
Famous quotes containing the words formal and/or definition:
“On every formal visit a child ought to be of the party, by way of provision for discourse.”
—Jane Austen (1775–1817)
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)