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# Riemannian-geometry

noun, Geometry.
1.
Also called elliptic geometry. the branch of non-Euclidean geometry that replaces the parallel postulate of Euclidean geometry with the postulate that in a plane every pair of distinct lines intersects.
Compare hyperbolic geometry.
2.
the differential geometry of a metric space that generalizes a Euclidean space.
Riemannian geometry
noun
1.
a branch of non-Euclidean geometry in which a line may have many parallels through a given point. It has a model on the surface of a sphere, with lines represented by great circles Also called elliptic geometry
Riemannian geometry
(rē-män’ē-ən)
A non-Euclidean system of geometry based on the postulate that within a plane every pair of lines intersects.

Tagged:

• Riemann-integral

noun, Mathematics. 1. integral (def 8a).

• Riemann-sphere

noun, Mathematics. 1. a sphere used for a stereographic projection.

• Riemann-Stieltjes integral

[ree-mahn-steel-chiz, -muh n] /ˈri mɑnˈstil tʃɪz, -mən/ noun, Mathematics. 1. the limit, as the norm of partitions of a given interval approaches zero, of the sum of the product of the first of two functions evaluated at some point in each subinterval multiplied by the difference in functional values of the second function at the […]

• Riemann-surface

noun, Mathematics. 1. a geometric representation of a function of a complex variable in which a multiple-valued function is depicted as a single-valued function on several planes, the planes being connected at some of the points at which the function takes on more than one value.

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