New hyper-Käahler structures on tangent bundles

Xuerong Qi; Linfen Cao; Xingxiao Li

Communications in Mathematics (2014)

  • Volume: 22, Issue: 1, page 13-30
  • ISSN: 1804-1388

Abstract

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Let ( M , g , J ) be an almost Hermitian manifold, then the tangent bundle T M carries a class of naturally defined almost hyper-Hermitian structures ( G , J 1 , J 2 , J 3 ) . In this paper we give conditions under which these almost hyper-Hermitian structures ( G , J 1 , J 2 , J 3 ) are locally conformal hyper-Kähler. As an application, a family of new hyper-structures is obtained on the tangent bundle of a complex space form. Furthermore, by restricting these almost hyper-Hermitian structures on the unit tangent sphere bundle T 1 M , we obtain a class of almost contact metric 3-structures. By virtue of these almost contact metric 3-structures, we find a family of Sasakian 3-structures on the unit tangent sphere bundle of a complex space form of positive holomorphic sectional curvature.

How to cite

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Qi, Xuerong, Cao, Linfen, and Li, Xingxiao. "New hyper-Käahler structures on tangent bundles." Communications in Mathematics 22.1 (2014): 13-30. <http://eudml.org/doc/261958>.

@article{Qi2014,
abstract = {Let $(M,g,J)$ be an almost Hermitian manifold, then the tangent bundle $TM$ carries a class of naturally defined almost hyper-Hermitian structures $(G,J_1,J_2,J_3)$. In this paper we give conditions under which these almost hyper-Hermitian structures $(G,J_1,J_2,J_3)$ are locally conformal hyper-Kähler. As an application, a family of new hyper-structures is obtained on the tangent bundle of a complex space form. Furthermore, by restricting these almost hyper-Hermitian structures on the unit tangent sphere bundle $T_1 M$, we obtain a class of almost contact metric 3-structures. By virtue of these almost contact metric 3-structures, we find a family of Sasakian 3-structures on the unit tangent sphere bundle of a complex space form of positive holomorphic sectional curvature.},
author = {Qi, Xuerong, Cao, Linfen, Li, Xingxiao},
journal = {Communications in Mathematics},
keywords = {tangent bundles; locally conformal hyper-Kähler structures; almost contact metric 3-structures; Sasakian 3-structures; tangent bundles; locally conformal hyper-Kähler structures; almost contact metric 3-structures; Sasakian 3-structures},
language = {eng},
number = {1},
pages = {13-30},
publisher = {University of Ostrava},
title = {New hyper-Käahler structures on tangent bundles},
url = {http://eudml.org/doc/261958},
volume = {22},
year = {2014},
}

TY - JOUR
AU - Qi, Xuerong
AU - Cao, Linfen
AU - Li, Xingxiao
TI - New hyper-Käahler structures on tangent bundles
JO - Communications in Mathematics
PY - 2014
PB - University of Ostrava
VL - 22
IS - 1
SP - 13
EP - 30
AB - Let $(M,g,J)$ be an almost Hermitian manifold, then the tangent bundle $TM$ carries a class of naturally defined almost hyper-Hermitian structures $(G,J_1,J_2,J_3)$. In this paper we give conditions under which these almost hyper-Hermitian structures $(G,J_1,J_2,J_3)$ are locally conformal hyper-Kähler. As an application, a family of new hyper-structures is obtained on the tangent bundle of a complex space form. Furthermore, by restricting these almost hyper-Hermitian structures on the unit tangent sphere bundle $T_1 M$, we obtain a class of almost contact metric 3-structures. By virtue of these almost contact metric 3-structures, we find a family of Sasakian 3-structures on the unit tangent sphere bundle of a complex space form of positive holomorphic sectional curvature.
LA - eng
KW - tangent bundles; locally conformal hyper-Kähler structures; almost contact metric 3-structures; Sasakian 3-structures; tangent bundles; locally conformal hyper-Kähler structures; almost contact metric 3-structures; Sasakian 3-structures
UR - http://eudml.org/doc/261958
ER -

References

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