An anti-Kählerian Einstein structure on the tangent bundle of a space form

Tom 103 / 2005

Vasile Oproiu, Neculai Papaghiuc Colloquium Mathematicum 103 (2005), 41-46 MSC: Primary 53C55, 53C15, 53C05. DOI: 10.4064/cm103-1-6


In [11] we have considered a family of almost anti-Hermitian structures $(G,J)$ on the tangent bundle $TM$ of a Riemannian manifold $(M,g)$, where the almost complex structure $J$ is a natural lift of $g$ to $TM$ interchanging the vertical and horizontal distributions $VTM$ and $HTM$ and the metric $G$ is a natural lift of $g$ of Sasaki type, with the property of being anti-Hermitian with respect to $J$. Next, we have studied the conditions under which $(TM, G, J)$ belongs to one of the eight classes of anti-Hermitian structures obtained in the classification in [2]. In this paper, we study some geometric properties of the anti-Kählerian structure obtained in [11]. In fact we prove that it is Einstein. This result offers nice examples of anti-Kählerian Einstein manifolds studied in [1].


  • Vasile OproiuV. Oproiu
    Faculty of Mathematics
    University “Al. I. Cuza”
    Iaşi, Romania
  • Neculai PapaghiucN. Papaghiuc
    Department of Mathematics
    Technical University
    Iaşi, Romania

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