Universität Stuttgart

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Author: search.filters.author.Semmelmann, Uwe

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    Stability of compact symmetric spaces
    (2022) Semmelmann, Uwe; Weingart, Gregor
    In this article, we study the stability problem for the Einstein-Hilbert functional on compact symmetric spaces following and completing the seminal work of Koiso on the subject. We classify in detail the irreducible representations of simple Lie algebras with Casimir eigenvalue less than the Casimir eigenvalue of the adjoint representation and use this information to prove the stability of the Einstein metrics on both the quaternionic and Cayley projective plane. Moreover, we prove that the Einstein metrics on quaternionic Grassmannians different from projective spaces are unstable.
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    Deformations of nearly G2 structures
    (2021) Nagy, Paul‐Andi; Semmelmann, Uwe
    We describe the second order obstruction to deformation for nearly G2 structures on compact manifolds. Building on work of Alexandrov and Semmelmann, this allows proving rigidity under deformation for the proper nearly G2 structure on the Aloff–Wallach space N(1,1).
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    On the ergodicity of the frame flow on even-dimensional manifolds
    (2024) Cekić, Mihajlo; Lefeuvre, Thibault; Moroianu, Andrei; Semmelmann, Uwe
    It is known that the frame flow on a closed n-dimensional Riemannian manifold with negative sectional curvature is ergodic if nis odd and n≠7. In this paper we study its ergodicity in the remaining cases. For neven and n≠8,134, we show that: if n≡2mod 4 or n=4, the frame flow is ergodic if the manifold is ∼0.3-pinched, if n≡0mod 4, it is ergodic if the manifold is ∼0.6-pinched. In the three dimensions n=7,8,134, the respective pinching bounds that we need in order to prove ergodicity are 0.4962..., 0.6212..., and 0.5788.... This is a significant improvement over the previously known results and a step forward towards solving a long-standing conjecture of Brin asserting that 0.25-pinched even-dimensional manifolds have an ergodic frame flow.