Search Results for ""

For any sequence of integers 0<n_1<...<n_k, there is a flag manifold of type (n_1, ..., n_k) which is the collection of ordered sets of vector subspaces of R^(n_k) (V_1, ..., ...

The Stiefel manifold of orthonormal k-frames in R^n is the collection of vectors (v_1, ..., v_k) where v_i is in R^n for all i, and the k-tuple (v_1, ..., v_k) is ...

If W is a simply connected, compact manifold with a boundary that has two components, M_1 and M_2, such that inclusion of each is a homotopy equivalence, then W is ...

An Anosov diffeomorphism is a C^1 diffeomorphism phi of a manifold M to itself such that the tangent bundle of M is hyperbolic with respect to phi. Very few classes of Anosov ...

An ambient isotopy from an embedding of a manifold M in N to another is a homotopy of self diffeomorphisms (or isomorphisms, or piecewise-linear transformations, etc.) of N, ...

Let M^n be a compact n-dimensional oriented Riemannian manifold without boundary, let O be a group representation of pi_1(M) by orthogonal matrices, and let E(O) be the ...

A metric space X is isometric to a metric space Y if there is a bijection f between X and Y that preserves distances. That is, d(a,b)=d(f(a),f(b)). In the context of ...

A phase curve (i.e., an invariant manifold) which meets a hyperbolic fixed point (i.e., an intersection of a stable and an unstable invariant manifold) or connects the ...

An atlas is a collection of consistent coordinate charts on a manifold, where "consistent" most commonly means that the transition functions of the charts are smooth. As the ...

The notion of parallel transport on a manifold M makes precise the idea of translating a vector field V along a differentiable curve to attain a new vector field V^' which is ...