Sentence examples for be a connected manifold from inspiring English sources

Let M be a connected manifold and G be a closed Lie subgroup of GL V)—the general linear group on a finite dimensional vector space V. Denote by (Ωm) the space of H1-loops in M starting at a fixed point (m).

Let M, dim M=n≥3, be a connected semi-Riemannian smooth manifold endowed with a semi-Riemannian metric g of signature (s,n−s), 0≤s≤n.

Let Ω be a connected bounded domain in the gradient product Ricci soliton ((Sigmatimes mathbb {R}, langle,rangle, e^{-frac{kappa t^{2}}{2}},dnu,kappa )), where Σ is an Einstein manifold with constant Ricci curvature κ.

A subRiemannian manifold as a triplet ((M,Delta, g_0)) where M is a connected, smooth manifold of dimension (nin mathbb {N},Deltaa ) denotes a subbundle of TM bracket-generating TM, and (g_0) is a positive definite smooth, bilinear form on (Delta ), see for instance [66].

Let M be a smooth connected manifold endowed with a smooth measure μ and a smooth locally subelliptic diffusion operator L which is symmetric with respect to μ.

The space (mathfrak{B}_{v}^{mathbb{C} }) is a connected and real manifold of dimension (2delta^{2} v)) over the number field (mathbb{R} ).

The space (mathfrak{B}_{v}^{mathbb{C} }) of complex vertex conditions at vertex v is a connected and compact complex manifold of complex dimension (delta^{2} v)).

We answer completely this question for the cases in which is a connected, locally path connected and semilocally simply connected space, and and are manifolds either compact or triangulable.

A topological manifold is a connected, second-countable Hausdorff topological space which is locally Euclidean.

There is a connected point here.

4) Connected component: A connected component is a connected sub-graph of graph G.