1. This cannot be done with the ordinary Euclidean metric . 2. The boundaries of these neighborhoods are quotients of horospheres and thus have Euclidean metrics . 3. Just as Euclidean space uses a Euclidean metric , so spacetime uses a Minkowski metric. 4. The Minkowski metric is not a Euclidean metric , because it is indefinite ( see metric signature ). 5. For parallel transport on a sphere, the implicit dependence is intrinsic to the non-euclidean metric . 6. The Euclidean metric defines the distance between two points as the length of the straight line connecting them. 7. The Euclidean metric defines the distance between two points as the length of the straight line segment connecting them. 8. Remember, to measure all distances, I am using Euclidean metric , NOT the taxi-cab metric. 9. The seventh cross product is for the Pauli spin in the 3-dimensional space with the Euclidean metric . 10. This embedding induces a metric on the sphere, it is inherited directly from the Euclidean metric on the ambient space.
Mobile