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A strong pseudo-Riemannian metric on a smooth manifold M is a (0,2) tensor field g which is symmetric and for which, at each m in M, the map v_m|->g_m(v_m,·) is an ...
Euclidean n-space is denoted R^n.
A hyperbolic version of the Euclidean cube.
A hyperbolic version of the Euclidean icosahedron.
A strong Riemannian metric on a smooth manifold M is a (0,2) tensor field g which is both a strong pseudo-Riemannian metric and positive definite. In a very precise way, the ...
A weak Riemannian metric on a smooth manifold M is a (0,2) tensor field g which is both a weak pseudo-Riemannian metric and positive definite. In a very precise way, the ...
A hyperbolic version of the Euclidean tetrahedron.
The taxicab metric, also called the Manhattan distance, is the metric of the Euclidean plane defined by g((x_1,y_1),(x_2,y_2))=|x_1-x_2|+|y_1-y_2|, for all points ...
The concept of a space is an extremely general and important mathematical construct. Members of the space obey certain addition properties. Spaces which have been ...
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