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

Vasile Oproiu, and Neculai Papaghiuc. "An anti-Kählerian Einstein structure on the tangent bundle of a space form." Colloquium Mathematicae 103.1 (2005): 41-46. <http://eudml.org/doc/283749>.

@article{VasileOproiu2005,
abstract = {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].},
author = {Vasile Oproiu, Neculai Papaghiuc},
journal = {Colloquium Mathematicae},
keywords = {tangent bundle; anti-Hermitian; almost complex structure; anti-Kählerian Einstein manifolds; Riemannian manifold},
language = {eng},
number = {1},
pages = {41-46},
title = {An anti-Kählerian Einstein structure on the tangent bundle of a space form},
url = {http://eudml.org/doc/283749},
volume = {103},
year = {2005},
}

TY - JOUR
AU - Vasile Oproiu
AU - Neculai Papaghiuc
TI - An anti-Kählerian Einstein structure on the tangent bundle of a space form
JO - Colloquium Mathematicae
PY - 2005
VL - 103
IS - 1
SP - 41
EP - 46
AB - 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].
LA - eng
KW - tangent bundle; anti-Hermitian; almost complex structure; anti-Kählerian Einstein manifolds; Riemannian manifold
UR - http://eudml.org/doc/283749
ER -