From Sasakian 3-structures to quaternionic geometry

Yoshiyuki Watanabe; Hiroshi Mori

Archivum Mathematicum (1998)

  • Volume: 034, Issue: 3, page 379-386
  • ISSN: 0044-8753

Abstract

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We construct a family of almost quaternionic Hermitian structures from an almost contact metric 3-structure and also do three kinds of quaternionic Kähler structures from a Sasakian 3-structure. In particular we have a generalization of the second main result of Boyer-Galicki-Mann [5].

How to cite

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Watanabe, Yoshiyuki, and Mori, Hiroshi. "From Sasakian 3-structures to quaternionic geometry." Archivum Mathematicum 034.3 (1998): 379-386. <http://eudml.org/doc/248177>.

@article{Watanabe1998,
abstract = {We construct a family of almost quaternionic Hermitian structures from an almost contact metric 3-structure and also do three kinds of quaternionic Kähler structures from a Sasakian 3-structure. In particular we have a generalization of the second main result of Boyer-Galicki-Mann [5].},
author = {Watanabe, Yoshiyuki, Mori, Hiroshi},
journal = {Archivum Mathematicum},
keywords = {almost contact metric 3-structure; Sasakian 3-structure; almost quaternionic Hermitian manifold; quaternionic Kähler manifold; hyperkähler manifold; almost contact metric 3-structure; Sasakian 3-structure; almost quaternionic Hermitian manifold; quaternionic Kähler manifold; hyperkähler manifold},
language = {eng},
number = {3},
pages = {379-386},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {From Sasakian 3-structures to quaternionic geometry},
url = {http://eudml.org/doc/248177},
volume = {034},
year = {1998},
}

TY - JOUR
AU - Watanabe, Yoshiyuki
AU - Mori, Hiroshi
TI - From Sasakian 3-structures to quaternionic geometry
JO - Archivum Mathematicum
PY - 1998
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 034
IS - 3
SP - 379
EP - 386
AB - We construct a family of almost quaternionic Hermitian structures from an almost contact metric 3-structure and also do three kinds of quaternionic Kähler structures from a Sasakian 3-structure. In particular we have a generalization of the second main result of Boyer-Galicki-Mann [5].
LA - eng
KW - almost contact metric 3-structure; Sasakian 3-structure; almost quaternionic Hermitian manifold; quaternionic Kähler manifold; hyperkähler manifold; almost contact metric 3-structure; Sasakian 3-structure; almost quaternionic Hermitian manifold; quaternionic Kähler manifold; hyperkähler manifold
UR - http://eudml.org/doc/248177
ER -

References

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  1. Alekseevsky D. V., Marchiafava S., Almost quaternionic Hermitian and quasi-Kähler manifolds, Proceedings of the International Workshop on Almost Complex Manifolds (Sofia, 22-25 Agosto 1993) 150-175. (1993) MR1375931
  2. Bär C., Real Killing spinors and holonomy, Comm. Math. Phys. 154(1993) 509-521. (1993) MR1224089
  3. Blair D. E., Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. (509, Springer Verlarg, Berlin-Heidelberg-New York, 1976). (1976) Zbl0319.53026MR0467588
  4. Boyer C. P., Galicki K., Mann B. M., Quaternionic reduction and Einstein manifolds, Comm. Anal. Geom. 1(2)(1993) 229-279. (1993) Zbl0856.53038MR1243524
  5. Boyer C. P., Galicki K., Mann B. M., The geometry and topology of 3-Sasakian manifolds, J. Reine Angew. Math. 455(1994) 183-220. (1994) Zbl0889.53029MR1293878
  6. Ejiri N., A generalization of minimal cones, Trans. Amer. Math. Soc. 276(1983) 347-360. (1983) Zbl0511.53063MR0684514
  7. Hsiang W. Y., On the laws of trigonometries of two-point homogeneous spaces, Ann. Global Anal. Geom. 7(1989) 29-45. (1989) Zbl0695.53036MR1029843
  8. Ishihara S., Quaternion Kählerian manifolds, J. Differential Geom. 9(1974) 483-500. (1974) Zbl0297.53014MR0348687
  9. Kashiwada T., A note on a Riemannian spaces with Sasakian 3-structure, Nat. Sci. Rep. Ochanomizu Univ. 22(1971) 1-2. (1971) MR0303449
  10. Konishi M., On manifolds with Sasakian 3-structure over quaternion Kählerian manifolds, Kōdai Math. Sem. Rep. 26(1975) 194-200. (1975) MR0377782
  11. Kuo Y. Y., On almost contact 3-structure, Tôhoku Math. J. 22(1970) 325-332. (1970) Zbl0205.25801MR0278225
  12. Nakashima Y., Watanabe Y., Some constructions of almost Hermitian and quaternion metric structures, Math. J. Toyama Univ. 13(1990) 119-138. (1990) Zbl0722.53027MR1089079
  13. Tachibana S., Yu W. N., On a Riemannian space admitting more than one Sasakian structure, Tôhoku Math. J. 22(1970) 536-540. (1970) MR0275329
  14. Tanno S., Killing vectors on contact Riemannian manifolds and fiberings related to the Hopf fibrations, Tôhoku Math. J. 23(1971) 313-333. (1971) MR0287477
  15. Watanabe Y., Mori H., Geometry on unitary-symmetric Kähler manifolds, Math. J. Toyama Univ. 16(1983) 135-193. (1983) MR1255450

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