Tangent Space

Let x be a point in an n-dimensional compact manifold M, and attach at x a copy of R^n tangential to M. The resulting structure is called the tangent space of M at x and is denoted T_xM. If gamma is a smooth curve passing through x, then the derivative of gamma at x is a vector in T_xM.

See also

Chart Tangent Space, Submanifold Tangent Space, Tangent, Tangent Bundle, Tangent Plane, Tangent Vector Explore this topic in the MathWorld classroom

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Cite this as:

Weisstein, Eric W. "Tangent Space." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TangentSpace.html

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