From Sasakian 3-structures to quaternionic geometry
Archivum mathematicum, Tome 34 (1998) no. 3, pp. 379-386 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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].
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].
Classification : 53C25, 53C26
Keywords: almost contact metric 3-structure; Sasakian 3-structure; almost quaternionic Hermitian manifold; quaternionic Kähler manifold; hyperkähler manifold
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Watanabe, Yoshiyuki; Mori, Hiroshi. From Sasakian 3-structures to quaternionic geometry. Archivum mathematicum, Tome 34 (1998) no. 3, pp. 379-386. http://geodesic.mathdoc.fr/item/ARM_1998_34_3_a5/

[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. | MR

[2] Bär C.: Real Killing spinors and holonomy. Comm. Math. Phys. 154(1993) 509-521. | MR

[3] Blair D. E.: Contact Manifolds in Riemannian Geometry. Lecture Notes in Math. (509, Springer Verlarg, Berlin-Heidelberg-New York, 1976). | MR | Zbl

[4] Boyer C. P., Galicki K., Mann B. M.: Quaternionic reduction and Einstein manifolds. Comm. Anal. Geom. 1(2)(1993) 229-279. | MR | Zbl

[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. | MR | Zbl

[6] Ejiri N.: A generalization of minimal cones. Trans. Amer. Math. Soc. 276(1983) 347-360. | MR | Zbl

[7] Hsiang W. Y.: On the laws of trigonometries of two-point homogeneous spaces. Ann. Global Anal. Geom. 7(1989) 29-45. | MR | Zbl

[8] Ishihara S.: Quaternion Kählerian manifolds. J. Differential Geom. 9(1974) 483-500. | MR | Zbl

[9] Kashiwada T.: A note on a Riemannian spaces with Sasakian 3-structure. Nat. Sci. Rep. Ochanomizu Univ. 22(1971) 1-2. | MR

[10] Konishi M.: On manifolds with Sasakian 3-structure over quaternion Kählerian manifolds. Kōdai Math. Sem. Rep. 26(1975) 194-200. | MR

[11] Kuo Y. Y.: On almost contact 3-structure. Tôhoku Math. J. 22(1970) 325-332. | MR | Zbl

[12] Nakashima Y., Watanabe Y.: Some constructions of almost Hermitian and quaternion metric structures. Math. J. Toyama Univ. 13(1990) 119-138. | MR | Zbl

[13] Tachibana S., Yu W. N.: On a Riemannian space admitting more than one Sasakian structure. Tôhoku Math. J. 22(1970) 536-540. | MR

[14] Tanno S.: Killing vectors on contact Riemannian manifolds and fiberings related to the Hopf fibrations. Tôhoku Math. J. 23(1971) 313-333. | MR

[15] Watanabe Y., Mori H.: Geometry on unitary-symmetric Kähler manifolds. Math. J. Toyama Univ. 16(1983) 135-193. | MR