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].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-6,
author = {Vasile Oproiu and Neculai Papaghiuc},
title = {An anti-K\"ahlerian Einstein structure on the tangent bundle of a space form},
journal = {Colloquium Mathematicae},
volume = {103},
year = {2005},
pages = {41-46},
zbl = {1077.53028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-6}
}
Vasile Oproiu; Neculai Papaghiuc. An anti-Kählerian Einstein structure on the tangent bundle of a space form. Colloquium Mathematicae, Tome 103 (2005) pp. 41-46. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-6/