Riemannian Manifold
In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real smooth manifold M equipped with an inner product on each tangent space that varies smoothly from point to point in the sense that if X and Y are vector fields on M, then is a smooth function. The family of inner products is called a Riemannian metric (tensor). These terms are named after the German mathematician Bernhard Riemann. The study of Riemannian manifolds comprises the subject called Riemannian geometry.
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Famous quotes containing the word manifold:
“They had met, and included in their meeting the thrust of the manifold grass stems, the cry of the peewit, the wheel of the stars.”
—D.H. (David Herbert)