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Metric geometries over the split quaternions

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Metric geometries over the split quaternions. / Dancer, A. S.; Jørgensen, Helge Riis; Swann, A. F.
In: Rendiconti del Seminario Matematico, Vol. 63, No. 2, 01.12.2005, p. 119-139.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Review › Research › peer-review

Harvard

Dancer, AS, Jørgensen, HR & Swann, AF 2005, 'Metric geometries over the split quaternions', Rendiconti del Seminario Matematico, vol. 63, no. 2, pp. 119-139.

APA

Dancer, A. S., Jørgensen, H. R., & Swann, A. F. (2005). Metric geometries over the split quaternions. Rendiconti del Seminario Matematico, 63(2), 119-139.

CBE

Dancer AS, Jørgensen HR, Swann AF. 2005. Metric geometries over the split quaternions. Rendiconti del Seminario Matematico. 63(2):119-139.

MLA

Dancer, A. S., Helge Riis Jørgensen, and A. F. Swann. "Metric geometries over the split quaternions". Rendiconti del Seminario Matematico. 2005, 63(2). 119-139.

Vancouver

Dancer AS, Jørgensen HR, Swann AF. Metric geometries over the split quaternions. Rendiconti del Seminario Matematico. 2005 Dec 1;63(2):119-139.

Author

Dancer, A. S. ; Jørgensen, Helge Riis ; Swann, A. F. / Metric geometries over the split quaternions. In: Rendiconti del Seminario Matematico. 2005 ; Vol. 63, No. 2. pp. 119-139.

Bibtex

@article{9293e31e21d849a0be9f8815455aaab9,
title = "Metric geometries over the split quaternions",
abstract = "We give an overview of some recent results in hypersymplectic and para-quaternionic K{\"a}hler geometry, and introduce the notion of split three-Sasakian manifold. In particular, we discuss the twistor spaces and Swann bundles of para-quaternionic K{\"a}hler manifolds. These are used to classify examples with a fully homogeneous action of a semi-simple Lie group, and to construct distinct para-quaternionic K{\"a}hler metrics from indefinite real analytic conformal manifolds. We also indicate how the theory of toric varieties gives rise to constructions of hypersymplectic manifolds.",
author = "Dancer, {A. S.} and J{\o}rgensen, {Helge Riis} and Swann, {A. F.}",
year = "2005",
month = dec,
day = "1",
language = "English",
volume = "63",
pages = "119--139",
journal = "Rendiconti del Seminario Matematico",
issn = "0373-1243",
publisher = "Rendiconti del Seminario Matematico",
number = "2",

}

RIS

TY - JOUR

T1 - Metric geometries over the split quaternions

AU - Dancer, A. S.

AU - Jørgensen, Helge Riis

AU - Swann, A. F.

PY - 2005/12/1

Y1 - 2005/12/1

N2 - We give an overview of some recent results in hypersymplectic and para-quaternionic Kähler geometry, and introduce the notion of split three-Sasakian manifold. In particular, we discuss the twistor spaces and Swann bundles of para-quaternionic Kähler manifolds. These are used to classify examples with a fully homogeneous action of a semi-simple Lie group, and to construct distinct para-quaternionic Kähler metrics from indefinite real analytic conformal manifolds. We also indicate how the theory of toric varieties gives rise to constructions of hypersymplectic manifolds.

AB - We give an overview of some recent results in hypersymplectic and para-quaternionic Kähler geometry, and introduce the notion of split three-Sasakian manifold. In particular, we discuss the twistor spaces and Swann bundles of para-quaternionic Kähler manifolds. These are used to classify examples with a fully homogeneous action of a semi-simple Lie group, and to construct distinct para-quaternionic Kähler metrics from indefinite real analytic conformal manifolds. We also indicate how the theory of toric varieties gives rise to constructions of hypersymplectic manifolds.

UR - http://www.scopus.com/inward/record.url?scp=33751538018&partnerID=8YFLogxK

M3 - Review

AN - SCOPUS:33751538018

VL - 63

SP - 119

EP - 139

JO - Rendiconti del Seminario Matematico

JF - Rendiconti del Seminario Matematico

SN - 0373-1243

IS - 2

ER -