Article

Higher-dimensional Osserman metrics with non-nilpotent Jacobi operators

Geometriae Dedicata (Impact Factor: 0.47). 07/2010; DOI: 10.1007/s10711-011-9595-y
Source: arXiv

ABSTRACT We exhibit Osserman metrics with non-nilpotent Jacobi operators and with non-trivial Jordan normal form in neutral signature (n,n) for any n which is at least 3. These examples admit a natural almost para-Hermitian structure and are semi para-complex Osserman with non-trivial Jordan normal form as well; they neither satisfy the third Gray identity nor are they integrable.

Full-text

Available from: Esteban Calviño-Louzao, Feb 08, 2014
1 Follower
 · 
115 Views
  • Source
    Far East Journal of Mathematical Sciences 01/2014; 94(1):1-11.
  • [Show abstract] [Hide abstract]
    ABSTRACT: This book describes areas of differential geometry related to affine geometry, such as Walker structures, Riemannian extensions, and (para-)Kähler-Weyl geometry. Affine connections arise naturally in conformal geometry. One can associate a pseudo-Riemannian structure to a given affine connection. The authors use this correspondence to study the geometry of both objects. The book is accessible to graduate students who have taken a core course in differential geometry, as well as to researchers from other disciplines. The basic definitions and results are introduced in the first chapter. It includes a lot of proofs. Chapters 2 and 3 study the geometry of deformed and modified Riemannian extensions. The fourth chapter is devoted to the study of Kähler-Weyl geometry. The book also includes a lot of historical references. Table of Contents: Basic notions and concepts; The geometry of deformed Riemannian extensions; The geometry of modified Riemannian extensions; (Para-)Kähler-Weyl manifolds.
    Synthesis Lectures on Mathematics and Statistics 05/2013; 6(1). DOI:10.2200/S00502ED1V01Y201305MAS013
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: An affine manifold ( M , ∇ ) is affine Osserman if the eigenvalues of the affine Jacobi operators vanish. In the present paper, we exhibit examples of affine Osserman connections which are Ricci flat and which are not Ricci flat on R3.
    Far East Journal of Mathematical Sciences 12/2014; 94(1):1-11.