Читать книгу Riemannian space. Recognition of formulas (structures) of riemannian manifolds by a neural network - Ludmila Naumova - Страница 5

Einstein used the concept of extended quantities in his theory of relativity. His feature in the theory of relativity is Minkowski’s four-dimensional world “space-time continuum”, just the spread of Riemann’s ideas of the extended concept of manifolds. This is a Riemann variety, where a three-fold extended space is combined with a fourth quantity, time. This is an example of a fourfold extended manifold with different values (space and time), and therefore different metrics. Einstein used a variety with values of different metrics. Why not spread it, generalize it, and go further? Why not construct a manifold with an arbitrary multiple extension (i.e., dimension), where the metric for each extension (dimension) can be different? After all, this is also a repeatedly extended space (diversity) in the broad sense of the word – it is a connected set on certain characteristics and characteristics are dimensions that have their own metric. Then the question “where in life, in the real world, are these diversity (spaces)?” no longer have. They are everywhere. Next, we’ll show you.