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December 2014 Construction of Complex Contact Manifolds via Reduction
Mitsuhiro IMADA
Tokyo J. Math. 37(2): 509-522 (December 2014). DOI: 10.3836/tjm/1422452806

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 $S^{4m+3} \times S^{4n+3}$.

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Mitsuhiro IMADA. "Construction of Complex Contact Manifolds via Reduction." Tokyo J. Math. 37 (2) 509 - 522, December 2014. https://doi.org/10.3836/tjm/1422452806

Information

Published: December 2014
First available in Project Euclid: 28 January 2015

zbMATH: 1327.53104
MathSciNet: MR3304694
Digital Object Identifier: 10.3836/tjm/1422452806

Rights: Copyright © 2014 Publication Committee for the Tokyo Journal of Mathematics

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Vol.37 • No. 2 • December 2014
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