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How to construct all metric f-K-contact manifolds

  • Oliver Goertsches and Eugenia Loiudice EMAIL logo
Published/Copyright: July 6, 2021
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Abstract

We show that any compact metric f-K-contact, respectively S-manifold is obtained from a compact K-contact, respectively Sasakian manifold by an iteration of constructions of mapping tori, rotations, and type II deformations.

MSC 2010: 53C25; 53D10
  1. Communicated by: T. Leistner

References

[1] G. Bazzoni, O. Goertsches, Toric actions in cosymplectic geometry. Forum Math. 31 (2019), 907–915. MR3975667 Zbl 1421.5307910.1515/forum-2018-0153Search in Google Scholar

[2] D. E. Blair, Geometry of manifolds with structural group 𝓤(n) × 𝓞(s). J. Differential Geometry4 (1970), 155–167. MR267501 Zbl 0202.2090310.4310/jdg/1214429380Search in Google Scholar

[3] D. E. Blair, G. D. Ludden, Hypersurfaces in almost contact manifolds. Tohoku Math. J. (2) 21 (1969), 354–362. MR251668 Zbl 0184.2550210.2748/tmj/1178242948Search in Google Scholar

[4] C. P. Boyer, K. Galicki, Sasakian geometry. Oxford Univ. Press 2008. MR2382957 Zbl 1155.5300210.1093/acprof:oso/9780198564959.001.0001Search in Google Scholar

[5] J. L. Cabrerizo, L. M. Fernández, M. Fernández, The curvature tensor fields on f-manifolds with complemented frames. An. Ştiinţ. Univ. Al. I. Cuza Iaşi Secţ. I a Mat. 36 (1990), 151–161. MR1109808 Zbl 0737.53031Search in Google Scholar

[6] O. Goertsches, E. Loiudice, On the topology of metric f-K-contact manifolds. Monatsh. Math. 192 (2020), 355–370. MR4098147 Zbl 0720787010.1007/s00605-020-01400-zSearch in Google Scholar

[7] P. Molino, Riemannian foliations. Birkhäuser Boston, Inc., Boston, MA 1988. MR932463 Zbl 0633.5300110.1007/978-1-4684-8670-4Search in Google Scholar

[8] K. Yano, On a structure defined by a tensor field f of type (1, 1) satisfying f3 + f = 0. Tensor (N.S.) 14 (1963), 99–109. MR159296 Zbl 0122.4070510.1016/S0304-0208(08)72251-5Search in Google Scholar

Received: 2020-11-20
Published Online: 2021-07-06
Published in Print: 2021-10-26

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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