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Manuel Amann

  1. Partial Classification Results for Positive Quaternion Kaehler Manifolds.

    Wed, 11/25/2009 - 16:01 — SomNambul
    Authors: Manuel Amann
    Subjects: Differential Geometry
    Abstract

    Positive Quaternion Kaehler Manifolds are Riemannian manifolds with holonomy
    contained in Sp(n)Sp(1) and with positive scalar curvature. Conjecturally, they
    are symmetric spaces. We prove this conjecture in dimension 20 under additional
    assumptions and we provide recognition theorems for quaternionic projective
    spaces (in low dimensions) as well as the real Grassmanian (which is Positive
    Quaternion Kaehler).

  2. Formality of Positive Quaternion Kaehler Manifolds.

    Wed, 11/18/2009 - 16:01 — SomNambul
    Authors: Manuel Amann
    Subjects: General Topology
    Abstract

    Positive Quaternion Kaehler Manifolds are Riemannian manifolds with holonomy
    contained in Sp(n)Sp(1) and with positive scalar curvature. Conjecturally, they
    are symmetric spaces. We offer a new approach to this field of study via
    Rational Homotopy Theory, thereby proving the formality of Positive Quaternion
    Kaehler Manifolds. This result is established by means of an in-depth
    investigation on how formality behaves under spherical fibrations.

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