Sentence examples for manifold with a from inspiring English sources

Let M be a compact Riemannian manifold with a smooth C∞ boundary ∂M.

Thus, Penrose claims, we make a mistake to model the early universe by a Lorentzian manifold with a metric (as is done in classical general relativity).

Let E be the loop space over a compact connected Riemannian manifold with a torsion skew symmetric connection.

Several possible notions of Hardy Sobolev spaces on a Riemannian manifold with a doubling measure are considered.

However, the Stiefel manifold is not in general an attracting submanifold of the ambient Euclidean space: it is a constraint manifold with a weak numerical invariant.

It implies that data are disposed along a manifold with a dimensionality d less than dimensionality d o of the original data space.

Then, the M becomes a Riemannian manifold with an indefinite metric.

A principle example is the Laplace operator for a manifold with an asymptotically conic singularity.

The multilayer chip contains a trap-and-release immobilization manifold with an array of micro-mechanical traps that capture single fish embryos.

Let us define now the following surgery operation # n : carve n balls out of a manifold, copy the manifold with an opposite orientation, and identify the boundary of these balls pairwise.

end{aligned} (2.13) Let M̃ be a Kenmotsu manifold with an almost contact structure ((varphi, xi, eta)) and M be a submanifold tangent to the structure vector field ξ isometrically immersed in M̃.