Sentence examples for be a smooth compact from inspiring English sources

Let be a smooth, compact Riemannian -manifold.

Let be a smooth, compact Riemannian manifold without boundary.

Let X be a smooth compact manifold with boundary.

Let be a smooth, compact Riemannian -manifold and a positive integer, strictly smaller than.

Let X Open image in new window be a smooth compact closed manifold of dimension n, and Y Open image in new window be a submanifold of X Open image in new window of dimension q.

Let M be a smooth, compact, orientable, weakly pseudoconvex manifold of dimension 3, embedded in CN (N⩾2), of codimension one or more, and endowed with the induced CR structure.

Let f be a smooth function with compact support.

Let χ be a smooth function with compact support on [ 0, ∞ ) such that χ ( r ) = 1 for r < 1.

Let F be a smooth vector bundle over a compact manifold X Open image in new window and ∂ a connection on F. This is a first-order differential operator C ∞ ( X, F ) → Ω 1 ( X, F ) Open image in new window on X Open image in new window, satisfying ∂(ωf)=dω f + ω ∂f for all f ∈ C ∞ ( X, F ) Open image in new window and ω ∈ C ∞ ( X ) Open image in new window.

Let (M,g) be a smooth Riemannian manifold and G a compact Lie group acting on M effectively and by isometries.

Let Ω be a smooth domain (bounded or unbounded) with compact boundary or (Omega={mathbb{R}}^{n}_={x=(x_{1},ldots,ldots, x_{n}) in{mathbb{R}}^{n}: x_{n}>0}) ((ngeq3)) be the upper half space and let (G x,y)) be the Green function of the Laplacian ((-Delta)) on Ω with Dirichlet boundary conditions.