Sentence examples for main geometric objects from inspiring English sources

Let ((M,g,N)) be a normalized null hypersurface of a pseudo-Riemannian manifold ((overline{M}^{n+2},overline{g})), ∇ the induced connection on M. In order to relate the main geometric objects of both null and associated non-degenerate geometry on the null hypersurface, we first need to relate the covariant derivatives (nabla^{eta}) and ∇.

Therefore, the introduction of the main induced geometric objects on M as the Levi-Civita connection, the second fundamental form, the operator form, have different properties from the non-degenerate case.

Length, area, and volume, Dimensional measures of one-, two-, and three-dimensional geometric objects.

In general, by ignoring geometric measurements such as distances and angles, projective geometry enables a clearer understanding of some more generic properties of geometric objects.

For example, one might hold that geometric objects, such as circles, are regions of actual physical space.

At first glance, Carcione's simple ballpoint-pen drawings of geometric objects did not seem so impressive -- they looked like preparatory sketches for a still-life painting.

"You wouldn't be able to make such complex and very geometric objects," she explains.

Geometric algorithms are based on geometric objects such as points, lines and circles.

Each solution is a geometric construction which is considered a function receiving geometric objects (input) and returning other geometric objects (output).

The phantom includes both geometric objects and anatomic contours, and includes both positive (standing out) and negative (embedded in) objects.

Fractals are the geometric objects that are constructed by repeating geometric patterns at a smaller and smaller scale.