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Curved space - Wikipedia
Curved space often refers to a spatial geometry which is not "flat", where a flat space has zero curvature, as described by Euclidean geometry. [1] Curved spaces can generally be described by Riemannian geometry, though some simple cases can be described in other ways.
Shape of the universe - Wikipedia
The curvature of the universe places constraints on the topology. If the spatial geometry is spherical, i.e., possess positive curvature, the topology is compact. For a flat (zero curvature) or a hyperbolic (negative curvature) spatial geometry, the topology can be …
42 Curved Space - The Feynman Lectures on Physics
In general, we mean by a curved space simply one in which the rules of Euclidean geometry break down with one sign of discrepancy or the other. The amount of curvature—defined, say, by the excess radius—may vary from place to place.
What is the shape of the universe? - NASA
If space itself is curved, there are three general possibilities for the geometry of the universe. Each of these possibilites is tied to the amount of mass (and thus to the total strength of gravitation) in the universe, and each implies a different past and future for the universe.
Curvature of Space | Is space flat or curved? - Sky & Telescope
2014年8月8日 · According to Einstein’s theory of general relativity, massive objects warp the spacetime around them, and the effect a warp has on objects is what we call gravity. So, locally, spacetime is curved around every object with mass. Closed universe (top), open universe (middle), and flat universe (bottom).
Introduction to Astronomy - Weber State University
The curvature of space. Locally, space curves in response to mass, so it makes sense to think that the density of mass in the Universe would determine the universal curvature. If the density of the Universe is large, the Universe is positively curved.
The Curvature of the Universe Background - Department of …
In other words, the curvature of space, like the curvature of the Earth is directly linked to the gravity which tells matter how to move. We can also reinterpret our three scenarios to describe the curvature of the universe,
The CMB and the Curvature of Space - Physics LibreTexts
General relativity predicts that matter and energy curve spacetime. This idea of curvature applies to not just the space around individual objects but also the Universe as a whole; the entire matter and energy content of the Universe will bend the spacetime of the Universe as a whole.
The Curvature of Space - Scientific American
The Curvature of Space Just 100 years ago the young Bernhard Riemann gave his famed paper on the foundations of geometry. He discussed space of four or more dimensions, and paved the way for...
1854: Riemann’s classic lecture on curved space
The Riemann curvature tensor is simply a collection of numbers at every point in space that describes its curvature. Riemann went on to make valuable contributions to analysis, number theory, and complex manifold theory, among other areas.