Let f : M [right arrow] R be a function defined on the differential manifold M.
Furthermore, according to the definition of differential manifold, if M is [C.
In [Mac93], MacPherson introduced the notion of combinatorial differential manifold, a simplicial pseudo-manifold with an additional discrete structure--described in the language of oriented matroids--to model "the tangent bundle.
In [Mac93], motivated by his theory of combinatorial differential manifolds, MacPherson introduced the matroid Grassmannian (also called the MacPhersonian) MacP(d, n), which is the poset of rank d oriented matroids on [n] ordered by specialization.
Let (N, h) be a Riemannian manifold of dimension m and let M be a differential manifold of dimension n.
We start with a Riemannian manifold (N, h) of dimension m, a differential manifold M of dimension n, a [C.
Thus from a result of Yau  if M is a complete simply connected 3-D differential manifold with sectional curvature K < 0 one has for u 2 D(M)
1 Let M be a bounded and simply connected 3-D differential manifold with a reasonable boundary [integral]M.
N] be a differential manifold (vector space) which is a direct product of N copies of [[PI].
Let A and B be two differential manifolds and G be a smooth mapping G : A [right arrow] B.
1 on a differential manifold
in such a way that the properties of self-concordant functions in Euclidean space are preserved.
The text is intended to serve as a link between basic undergraduate geometry and more theoretical geometry such as Riemann surfaces, differential manifolds
, algebraic topology, and Riemannian geometry.