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

• Autorzy: Vasile Oproiu , Neculai Papaghiuc
• Języki publikacji: EN

Abstrakty

EN

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].

Kategorie tematyczne

• 53C05: Connections, general theory
• 53C55: Hermitian and K\"ahlerian manifolds
• 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2005
• Tom: 103
• Numer: 1
• Strony: 41-46

Daty

wydano

2005

Twórcy

autor

Vasile Oproiu

• V. Oproiu, Faculty of Mathematics, University "Al. I. Cuza", Iaşi, Romania

autor

Neculai Papaghiuc

• N. Papaghiuc, Department of Mathematics, Technical University, Iaşi, Romania

Identyfikatory

DOI

10.4064/cm103-1-6