geometry. Curved spaces can generally be described by Riemannian geometry, though some simple cases can be described in other ways. Curved spaces play an...

In mathematical analysis, a space-filling curve is a curve whose range reaches every point in a higher dimensional region, typically the unit square (or...

embedding space, it is not necessary that a surface be embedded in a higher-dimensional space in order to be curved. Such an intrinsically curved two-dimensional...

formula, too, is readily generalized to curved spacetime by replacing partial derivatives with their curved-manifold counterparts, covariant derivatives...

mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be...

Newtonian gravitation is a theory of curved time. General relativity is a theory of curved time and curved space. Given G as the gravitational constant...

geometry, the Peano curve is the first example of a space-filling curve to be discovered, by Giuseppe Peano in 1890. Peano's curve is a surjective, continuous...

quantum field theory in curved spacetime (QFTCS) is an extension of quantum field theory from Minkowski spacetime to a general curved spacetime. This theory...

Sphereland: A Fantasy About Curved Spaces and an Expanding Universe is a 1965 translation of Bolland : een roman van gekromde ruimten en uitdijend heelal...

The Hilbert curve (also known as the Hilbert space-filling curve) is a continuous fractal space-filling curve first described by the German mathematician...

Stress–strain curve Space-filling curve Contract curve Cost curve Demand curve Aggregate demand curve Compensated demand curve Engel curve Hubbert curve Indifference...

geometry is used as a model of physical space, it is known as curved space. Even in curved space, Minkowski space is still a good description in an infinitesimal...

four-dimensional flat Minkowski space, and not curved space nor GR. It is possible to formulate quantum field theory in curved spacetime, yet even this still...

which space is conceived as curved, rather than flat, as in the Euclidean space. According to Albert Einstein's theory of general relativity, space around...

caused by spacetime being curved ("distorted"). It is a common misconception to attribute gravity to curved space; neither space nor time has an absolute...

up to less than 180°; such 3-dimensional space is locally modeled by a region of a hyperbolic space H3. Curved geometries are in the domain of non-Euclidean...

The curved space diamond structure is a patented modular building system representative of a diamond crystal enlarged 8 billion times. These playground...

the Dirac equation in curved spacetime is a generalization of the Dirac equation from flat spacetime (Minkowski space) to curved spacetime, a general Lorentzian...

two-dimensional spaces are often called planes, or, more generally, surfaces. These include analogs to physical spaces, like flat planes, and curved surfaces...

solve this problem by transforming the time-sliced flat-space path integral to curved space using a multivalued coordinate transformation (nonholonomic...

three-dimensional Euclidean space, which is flat. However, in mathematics Newton's laws of motion can be generalized to multidimensional and curved spaces. Often the term...

For a de Broglie–Bohm theory on curved space with spin, the spin space becomes a vector bundle over configuration space, and the potential in Schrödinger's...

Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's Elements, it was the three-dimensional...

that their equations of motion will take the same form in curved space that they do in flat space. A physical law expressed in a generally covariant fashion...

}=g_{\rho \zeta }R^{\zeta }{}_{\sigma \mu \nu }.} One can see the effects of curved space by comparing a tennis court and the Earth. Start at the lower right corner...

theoretical physicist Walter Gordon in 1923 to study the geometrical optics in curved space-time filled with moving dielectric materials. Let ua be the normalized...

Relativistic energy and momentum Space-time Curved space Chapters: The Theory of Gravitation (Vol. I, Chapter 7) Curved Space (Vol. II, Chapter 42) Electromagnetism...

accelerated along a curved path. de Sitter precession, a general-relativistic correction accounting for the Schwarzschild metric of curved space near a large...

together, the curvature and the torsion of a space curve are analogous to the curvature of a plane curve. For example, they are coefficients in the system...

inertial, but globally non-inertial. Due to the non-Euclidean geometry of curved space-time, there are no global inertial reference frames in general relativity...