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A non-Sasakian Lefschetz $ K$-contact manifold of Tievsky type


Authors: Beniamino Cappelletti-Montano, Antonio De Nicola, Juan Carlos Marrero and Ivan Yudin
Journal: Proc. Amer. Math. Soc. 144 (2016), 5341-5350
MSC (2010): Primary 53C25, 53D35
DOI: https://doi.org/10.1090/proc/13187
Published electronically: June 3, 2016
MathSciNet review: 3556276
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Abstract: We find a family of five dimensional completely solvable compact manifolds that constitute the first examples of $ K$-contact manifolds which satisfy the Hard Lefschetz Theorem and have a model of Tievsky type just as Sasakian manifolds but do not admit any Sasakian structure.


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Beniamino Cappelletti-Montano
Affiliation: Dipartimento di Matematica e Informatica, Università degli Studi di Cagliari, Via Ospedale 72, 09124 Cagliari, Italy
Email: b.cappellettimontano@gmail.com

Antonio De Nicola
Affiliation: CMUC, Department of Mathematics, University of Coimbra, 3001-501 Coimbra, Portugal
Email: antondenicola@gmail.com

Juan Carlos Marrero
Affiliation: Unidad Asociada ULL-CSIC “Geometría Diferencial y Mecánica Geométrica” Departamento de Matemáticas, Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de La Laguna, La Laguna, Tenerife, Spain
Email: jcmarrer@ull.edu.es

Ivan Yudin
Affiliation: CMUC, Department of Mathematics, University of Coimbra, 3001-501 Coimbra, Portugal
Email: yudin@mat.uc.pt

DOI: https://doi.org/10.1090/proc/13187
Received by editor(s): October 22, 2015
Received by editor(s) in revised form: February 15, 2016
Published electronically: June 3, 2016
Additional Notes: This work was partially supported by CMUC – UID/MAT/00324/2013, funded by the Portuguese Government through FCT/MEC and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020 (second and fourth author), by MICINN (Spain) grants MTM2012-34478 and MTM2015-64166-C2-2-P (second and third author), by Prin 2010/11 – Varietà reali e complesse: geometria, topologia e analisi armonica – Italy (first author), and by the exploratory research project in the frame of Programa Investigador FCT IF/00016/2013 (fourth author)
Communicated by: Michael Wolf
Article copyright: © Copyright 2016 American Mathematical Society