## Tokyo Journal of Mathematics

### Construction of Complex Contact Manifolds via Reduction

#### Abstract

Kobayashi [13] introduced complex contact manifolds as a variant of real contact manifolds. Later, Ishihara and Konishi [11] defined normality of complex contact manifolds as for Sasakian manifolds in real contact geometry. In this paper, we construct normal complex contact manifolds via reduction from hyperk\"{a}hler manifolds, and give a new example of normal complex contact manifolds. To check the normality for the new examples, we give a useful identity about sectional curvatures of normal complex contact manifolds. We also give an explicit example of a non-normal complex almost contact metric structure on $S^{4m+3} \times S^{4n+3}$.

#### Article information

Source
Tokyo J. Math., Volume 37, Number 2 (2014), 509-522.

Dates
First available in Project Euclid: 28 January 2015

https://projecteuclid.org/euclid.tjm/1422452806

Digital Object Identifier
doi:10.3836/tjm/1422452806

Mathematical Reviews number (MathSciNet)
MR3304694

Zentralblatt MATH identifier
1327.53104

#### Citation

IMADA, Mitsuhiro. Construction of Complex Contact Manifolds via Reduction. Tokyo J. Math. 37 (2014), no. 2, 509--522. doi:10.3836/tjm/1422452806. https://projecteuclid.org/euclid.tjm/1422452806

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