Previous |  Up |  Next

Article

Keywords:
almost contact metric 3-structure; Sasakian 3-structure; almost quaternionic Hermitian manifold; quaternionic Kähler manifold; hyperkähler manifold
Summary:
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].
References:
[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 1375931
[2] Bär C.: Real Killing spinors and holonomy. Comm. Math. Phys. 154(1993) 509-521. MR 1224089
[3] Blair D. E.: Contact Manifolds in Riemannian Geometry. Lecture Notes in Math. (509, Springer Verlarg, Berlin-Heidelberg-New York, 1976). MR 0467588 | Zbl 0319.53026
[4] Boyer C. P., Galicki K., Mann B. M.: Quaternionic reduction and Einstein manifolds. Comm. Anal. Geom. 1(2)(1993) 229-279. MR 1243524 | Zbl 0856.53038
[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 1293878 | Zbl 0889.53029
[6] Ejiri N.: A generalization of minimal cones. Trans. Amer. Math. Soc. 276(1983) 347-360. MR 0684514 | Zbl 0511.53063
[7] Hsiang W. Y.: On the laws of trigonometries of two-point homogeneous spaces. Ann. Global Anal. Geom. 7(1989) 29-45. MR 1029843 | Zbl 0695.53036
[8] Ishihara S.: Quaternion Kählerian manifolds. J. Differential Geom. 9(1974) 483-500. MR 0348687 | Zbl 0297.53014
[9] Kashiwada T.: A note on a Riemannian spaces with Sasakian 3-structure. Nat. Sci. Rep. Ochanomizu Univ. 22(1971) 1-2. MR 0303449
[10] Konishi M.: On manifolds with Sasakian 3-structure over quaternion Kählerian manifolds. Kōdai Math. Sem. Rep. 26(1975) 194-200. MR 0377782
[11] Kuo Y. Y.: On almost contact 3-structure. Tôhoku Math. J. 22(1970) 325-332. MR 0278225 | Zbl 0205.25801
[12] Nakashima Y., Watanabe Y.: Some constructions of almost Hermitian and quaternion metric structures. Math. J. Toyama Univ. 13(1990) 119-138. MR 1089079 | Zbl 0722.53027
[13] Tachibana S., Yu W. N.: On a Riemannian space admitting more than one Sasakian structure. Tôhoku Math. J. 22(1970) 536-540. MR 0275329
[14] Tanno S.: Killing vectors on contact Riemannian manifolds and fiberings related to the Hopf fibrations. Tôhoku Math. J. 23(1971) 313-333. MR 0287477
[15] Watanabe Y., Mori H.: Geometry on unitary-symmetric Kähler manifolds. Math. J. Toyama Univ. 16(1983) 135-193. MR 1255450
Partner of
EuDML logo