Hostname: page-component-77c89778f8-9q27g Total loading time: 0 Render date: 2024-07-16T22:14:31.720Z Has data issue: false hasContentIssue false

On 6-Dimensional Nearly Kähler Manifolds

Published online by Cambridge University Press:  20 November 2018

Yoshiyuki Watanabe
Affiliation:
Unversity of Toyama, Department of Mathematics, Toyama 930-8555, Japan (Professor Emeritus) e-mail: sps99n69@snow.ocn.ne.jp
Young Jin Suh
Affiliation:
Kyungpook National University, Department of Mathematics, Taegu 702-701, Korea e-mail: yjsuh@knu.ac.kr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we give a sufficient condition for a complete, simply connected, and strict nearly Kähler manifold of dimension 6 to be a homogeneous nearly Kähler manifold. This result was announced in a previous paper by the first author.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2010

References

[1] Alexandrov, B., Grantcharov, G., and Ivanov, S., Curvature properties of twistor spaces of quaternionic Kähler manifolds. J. Geom. 62(1998), no. 1–2, 112. doi:10.1007/BF01237595Google Scholar
[2] Butruille, J. B., Classification des variétés approximativement kähleriennes homogènes. Ann. Glob. Anal. Geom. 27(2005), no. 3, 201225. doi:10.1007/s10455-005-1581-xGoogle Scholar
[3] Gray, A., Nearly Kähler manifolds. J. Differential Geometry 4(1970), 283309.Google Scholar
[4] Gray, A., Weak holonomy groups. Math. Z 123(1971), 290300. doi:10.1007/BF01109983Google Scholar
[5] Gray, A., The structure of nearly Kähler manifolds. Math. Ann. 223(1976), no. 3, 233248. doi:10.1007/BF01360955Google Scholar
[6] Grunewald, R., Six-dimensional Riemannian manifold with real Killing spinor. Ann. Global Anal. Geom. 8(1990), no. 1, 4359. doi:10.1007/BF00055017Google Scholar
[7] Kotô, S., Some theorems on almost Kählerian spaces. J. Math. Soc. Japan 12(1960), 422433. doi:10.2969/jmsj/01240422Google Scholar
[8] Matsumoto, M., On 6-dimensional almost Tachibana spaces. Tensor (N.S.) 23(1972), 250252.Google Scholar
[9] Moroianu, A., Nagy, P. A., and Semmelmann, U., Unit Killing vector fields on nearly Kähler manifolds. Internat. J. Math. 16(2005), no. 3, 281301. doi:10.1142/S0129167X05002874Google Scholar
[10] Nagy, P. A., On nearly Kähler geometry. Ann. Glob. Anal. Geom. 22(2002), no. 2, 167178. doi:10.1023/A:1019506730571Google Scholar
[11] Nagy, P. A., Nearly Kähler geometry and Riemannian foliations. Asian J. Math. 6(2002), no. 3, 481504.Google Scholar
[12] Tachibana, S., On almost-analytic vectors in certain almost-Hermitian manifolds. Tôhoku Math. J. 11(1959), 351363. doi:10.2748/tmj/1178244533Google Scholar
[13] Takamatsu, K., Some properties of 6-dimensional K-spaces. Kodai Math. Sem. Rep. 23(1971), 215232. doi:10.2996/kmj/1138846322Google Scholar
[14] Tricerri, F. and Vanhecke, L., Homogeneous structures on Riemannian manifolds. London Mathematical Society Lecture Note Series, 83, Cambridge University Press, Cambridge, 1983.Google Scholar
[15] Watanabe, Y. and Takamatsu, K., On a K-space of constant holomorphic sectional curvature. Kodai Math. Sem. Rep. 25(1973), 297306. doi:10.2996/kmj/1138846818Google Scholar
[16] Watanabe, Y., Six-dimensional nearly Kähler manifolds. In: Proceedings of The Eleventh International Workshop on Differential Geometry, Kyungpook Nat. Univ., Taegu, 2007, pp. 17.Google Scholar
[17] Yamaguchi, S., Chuman, O., and Matsumoto, M., On a special almost Tachibana space. Tensor (N.S.) 24(1972), 351354.Google Scholar
[18] Yano, K., Differential geometry on complex and almost complex spaces. International Series of Monographs in Pure and Applied Mathematics, 49, Pergamon Press, New York, 1965.Google Scholar