Riemannian manifold

In Riemannian geometry, a Riemannian manifold is a real differentiable manifold Manifold

A manifold is an abstract mathematical space [i] in which every point has a neighborho ... 

 M in which each tangent space is equipped with an inner product Inner product space

In mathematics [i], an inner product space is a vector space [i] with additional structure, an inner ... 

 g in a manner which varies smoothly from point to point. This allows one to define various notions such as angle Angle

An angle is the figure formed by two rays [i] sharing a common endpoint [i], called the vertex [i] ... 

s, lengths of curves, area Area

Area is a physical quantity [i] expressing the size of a part of a surface [i]. ... 

s, curvature Curvature

Curvature refers to a number of loosely related concepts in different areas of geometry.... 

, gradient Gradient

A generalization of these concepts is the gradient in vector calculus [i]; and this article is mostly ab ... 

s of functions and divergence of vector field Vector field

In mathematics [i] a vector field is a construction in vector calculus [i] which associates a vector [i] ... 

s.

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Encyclopedia

In Riemannian geometry, a Riemannian manifold is a real differentiable manifold Manifold

A manifold is an abstract mathematical space [i] in which every point has a neighborho ... 

 M in which each tangent space is equipped with an inner product Inner product space

In mathematics [i], an inner product space is a vector space [i] with additional structure, an inner... 

 g in a manner which varies smoothly from point to point. This allows one to define various notions such as angle Angle

An angle is the figure formed by two rays [i] sharing a common endpoint [i], called the vertex [i]... 

s, lengths of curves, area Area

Area is a physical quantity [i] expressing the size of a part of a surface [i]. ... 

s, curvature Curvature

Curvature refers to a number of loosely related concepts in different areas of geometry.... 

, gradient Gradient

A generalization of these concepts is the gradient in vector calculus [i]; and this article is mostly ab ... 

s of functions and divergence of vector field Vector field

In mathematics [i] a vector field is a construction in vector calculus [i] which associates a vector [i] ... 

s.
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