Displaying 101 – 120 of 212

Showing per page

Introduction to mean curvature flow

Roberta Alessandroni (2008/2009)

Séminaire de théorie spectrale et géométrie

This is a short overview on the most classical results on mean curvature flow as a flow of smooth hypersurfaces. First of all we define the mean curvature flow as a quasilinear parabolic equation and give some easy examples of evolution. Then we consider the M.C.F. on convex surfaces and sketch the proof of the convergence to a round point. Some interesting results on the M.C.F. for entire graphs are also mentioned. In particular when we consider the case of dimension one, we can compute the equation...

Invariance of g -natural metrics on linear frame bundles

Oldřich Kowalski, Masami Sekizawa (2008)

Archivum Mathematicum

In this paper we prove that each g -natural metric on a linear frame bundle L M over a Riemannian manifold ( M , g ) is invariant with respect to a lifted map of a (local) isometry of the base manifold. Then we define g -natural metrics on the orthonormal frame bundle O M and we prove the same invariance result as above for O M . Hence we see that, over a space ( M , g ) of constant sectional curvature, the bundle O M with an arbitrary g -natural metric G ˜ is locally homogeneous.

Invariant connections and invariant holomorphic bundles on homogeneous manifolds

Indranil Biswas, Andrei Teleman (2014)

Open Mathematics

Let X be a differentiable manifold endowed with a transitive action α: A×X→X of a Lie group A. Let K be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms of explicit finite dimensional quotients, of three classes of objects: equivalence classes of α-invariant K-connections on X α-invariant gauge classes of K-connections on X, andα-invariant isomorphism classes of pairs (Q,P) consisting of a holomorphic Kℂ-bundle Q → X and a K-reduction P of Q (when...

Currently displaying 101 – 120 of 212