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Jose Natario

  1. Relativity and Singularities - A Short Introduction for Mathematicians.

    Mon, 11/30/2009 - 16:01 — SomNambul
    Authors: Jose Natario
    Subjects: Differential Geometry
    Abstract

    We summarize the main ideas of General Relativity and Lorentzian geometry,
    leading to a proof of the simplest of the celebrated Hawking-Penrose
    singularity theorems. The reader is assumed to be familiar with Riemannian
    geometry and point set topology.

  2. An elementary derivation of the Montgomery phase formula for the Euler top.

    Mon, 09/14/2009 - 09:01 — SomNambul
    Authors: Jose Natario
    Subjects: Dynamical Systems
    Abstract

    We give an elementary derivation of the Montgomery phase formula for the
    motion of an Euler top, using only basic facts about the Euler equation and
    parallel transport on the 2-sphere (whose holonomy is seen to be responsible
    for the geometric phase). We also give an approximate geometric interpretation
    of the geometric phase for motions starting close to an unstable equilibrium
    point.

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