Infinitesimal Isometries on Compact Manifolds

On the infinitesimal isometries of manifolds with Killing spinors

We study the Lie algebra of infinitesimal isometries of 7–dimensional simply connected manifolds with Killing spinors. We obtain some splitting theorems for the action of this algebra on the space of Killing spinors, and as a corollary we prove that there are no infinitesimal isometry of constant length on a 7–dimensional 3– Sasakian manifold (not isometric to a space form) except the linear co...

Surgery on Compact Manifolds

Infinitesimal Isometries along Curves and Generalized Jacobi Equations

On a Riemannian manifold, a solution of the Killing equation is an infinitesimal isometry. Since the Killing equation is overdetermined, infinitesimal isometries do not exist in general. The complete prolongation of the Killing equation is a PDE on the bundle of 1-jets of vector fields. Restricted to a curve, it becomes an ODE that generalizes the Jacobi equation. A solution of this ODE is call...

Lipschitz Spaces on Compact Manifolds

Let f be a bounded function on the real line IF!. One may characterize the structural properties off by the modulus of smoothness w(t,f) = sup{lf (4 -f( y)l; x, y E 08, I x y I < t>, and, if w(t) is a continuous nondecreasing function of t > 0 such that w(O) = 0, by the Lipschitz class Lip(w) which is the set of all continuous functions such that su~~<~<i w(t, f)/o(t) < 00. It is possible to ex...

Expansive Homeomorphisms on Compact Manifolds

In this paper theorems are proved which provide for lifting and projecting expansive homeomorphisms through pseudocovering mappings so that the lift or projection is also an expansive homeomorphism. Using these techniques it is shown that the compact orientable surface of genus 2 admits an expansive homeomorphism.