Sentence examples for of a manifold from inspiring English sources

In 1911 he established his theorems on the invariance of the dimension of a manifold under continuous invertible transformations.

Betti's study of spaces of higher dimensions (greater than three) in the latter work did much to open up the subject, and it led the French mathematician Henri Poincaré to give the name Betti numbers to certain numbers that characterize the connectivity of a manifold (the higher-dimensional analog of a surface).

Another example of a manifold is face images [32].

The subsea manifold system is mainly comprised of a manifold and a foundation.

Consider an affine connection (nabla ) at a point (e) of a manifold (M).

In classical Lefschetz-Nielsen theory, one defines the Lefschetz invariant of an endomorphism of a manifold.

The topology determines the span of a manifold with respect to its connectivity and dimensionality.

Bitensor is a mathematical object that is defined in two distinct points of a manifold.

It is well known that the sectional curvatures of a manifold determine curvature tensor completely.

Let F1,…,Fr be a collection of smooth foliations of a manifold X.

Wolff understands beauty to consist in the perfection in things, which he understands in turn to consist in a harmony or order of a manifold.