, 2: For an OT manifold of type (s, t), all Betti numbers b l for 0 ? l ? s and for 2m ? s ? l ? 2m are positive

M. Abreu, Kähler-Sasaki geometry of toric symplectic cones in action-angle coordinates, Port. Math, vol.67, issue.2, pp.121-153, 2010.

V. Apostolov and G. Dloussky, Locally Conformally Symplectic Structures on Compact Non-Kähler Complex Surfaces, Int. Math. Res. Not, vol.9, pp.2717-2747, 2016.

V. Apostolov and G. Dloussky, On the Lee classes of locally conformally symplectic complex surfaces, to appear in, J. Symplectic Geom

D. Angella, A. Otiman, and N. Tardini, Cohomologies of locally conformally symplectic manifolds and solvmanifolds, vol.53, pp.67-96, 2018.

A. Beauville, Some remarks on Kähler manifolds with c 1 = 0, Prog. Math, vol.39, 1983.

A. Beauville, Variétés Kähleriennes dont la première classe de Chern est nulle, J. Diff. Geom, vol.18, pp.755-782, 1983.

F. Belgun, On the metric structure of non-Kähler complex surfaces, Math. Ann, vol.317, p.35, 2000.

F. Belgun and A. Moroianu, On the irreducibility of locally metric connections, J. Reine Angew. Math, vol.714, p.19, 2016.
URL : https://hal.archives-ouvertes.fr/hal-02102594

Y. Benoist, Actions Symplectiques de Groupes Compacts, vol.89, p.58, 2002.

A. Blanchard, Espaces fibrés kähleriens compacts, Comptes Rendus Acad. Sci, vol.238, pp.2281-2283, 1954.

F. A. Bogomolov, On Guan's examples of simply connected non-Kähler compact complex manifolds, Amer. J. Math, vol.118, pp.1037-1046, 1996.

S. Boissiére, M. Nieper-wißkirchen, and A. Sarti, Higher dimensional Enriques varieties and automorphisms of generalized Kummer varieties, J. Math. Pures Appl, vol.95, p.13, 2011.

E. Bombieri, Letter to Kodaira, p.35, 1973.

W. M. Boothby, Some fundamental formulas for Hermitian manifolds with vanishing torsion, American J. Math, vol.76, pp.509-534, 1954.

O. Braunling, Oeljeklaus-Toma manifolds and arithmetic invariants, Math. Z, vol.286, pp.291-323, 2017.

G. Bredon, Introduction to Compact Transformation Groups, Pure and Applied Mathematics, vol.46, p.58, 1972.

M. Brunella, Locally conformally Kähler metrics on certain non-Kählerian surfaces, Math. Ann, vol.346, p.36, 2010.

M. Brunella, Locally conformally Kähler metrics on Kato surfaces, Nagoya Math. J, vol.202, pp.77-81, 2011.

R. Bott and L. Tu, Differential forms in algebraic topology, p.71, 1982.
DOI : 10.1007/978-1-4757-3951-0

V. I. Danilov, The Geometry of Toric Varieties, = Uspekhi Mat. Nauk SSSR, vol.33, pp.85-134, 1978.
DOI : 10.1070/rm1978v033n02abeh002305

A. Dimca, Sheaves in topology, vol.75, 2003.
DOI : 10.1007/978-3-642-18868-8

A. Dubickas, Nonreciprocal units in a number field with an application to OT manifolds, New York J. Math, vol.20, pp.257-274, 2014.

J. J. Duistermaat and J. A. Kolk, Lie Groups, p.58, 2000.

M. Farber, Topology of closed one-form, Mathematical surveys and monographs, Amer. Math. Soc, vol.108, 2004.

A. Fujiki and M. Pontecorvo, Anti-self-dual bihermitian structures on Inoue surfaces, J. Diff. Geom, vol.85, pp.15-71, 2010.
DOI : 10.4310/jdg/1284557925

URL : https://doi.org/10.4310/jdg/1284557925

A. Fujiki and M. Pontecorvo, Bi-Hermitian metrics on Kato surfaces, p.36, 2016.

P. Gauduchon, La classe de Chern pluriharmonique d'un fibré en droites, C. R. Acad. Sci. Paris Sér. A-B, vol.282, issue.9, pp.479-482, 1976.

P. Gauduchon, Le théorème de l'excentricité nulle, C.R. Acad. Sci. Paris, vol.285, pp.387-390, 1977.

P. Gauduchon, La 1-forme de torsion d'une variété hermitienne compacte, Math. Ann, vol.267, p.22, 1984.
DOI : 10.1007/bf01455968

P. Gauduchon and L. Ornea, Locally Conformally Kähler Metrics on Hopf Surfaces, vol.48, pp.1107-1127, 1998.
DOI : 10.5802/aif.1651

URL : http://archive.numdam.org/article/AIF_1998__48_4_1107_0.pdf

R. Gini, L. Ornea, and M. Parton, Locally Conformal Kähler Reduction, J. Reine Angew. Math, vol.581, pp.1-21, 2005.
DOI : 10.1515/crll.2005.2005.581.1

URL : http://arxiv.org/pdf/math/0208208v1.pdf

R. Gini, L. Ornea, M. Parton, and P. Piccinni, Reduction of Vaisman structures in complex and quaternionic geometry, J. Geom. Phys, vol.56, issue.12, pp.2501-2522, 2006.

R. Goto, On the stability of locally conformal Kähler structures, J. Math. Soc. Japan, vol.66, issue.4, pp.1375-1401, 2014.

P. Griffiths and J. Harris, Principles of algebraic geometry, p.71, 1978.

D. Guan, Examples of compact holomorphic symplectic manifolds which admit no Kähler structure, Geometry and Analisys on Complex Manifolds -Festschrift for Professor Kobayashi S. 60th Birthday, pp.63-74, 1994.

S. Haller and T. Rybicki, Reduction for Locally Conformal Symplectic Manifolds, J. Geom. Phys, vol.37, issue.3, pp.262-271, 2001.
DOI : 10.1016/s0393-0440(00)00050-4

URL : http://www.mat.univie.ac.at/~stefan/files/red.pdf

M. Inoue, On surfaces of Class V II 0, Invent. Math, vol.24, pp.269-310, 1974.

M. Inoue, S. Kobayashi, and T. Ochiai, Holomorphic affine connections on compact complex surfaces, J. Fac. Sci. Univ. Tokyo Sect. IA Math, vol.27, issue.2, pp.247-264, 1980.

N. Istrati, Twisted holomorphic symplectic forms, Bull. London Math. Soc, vol.48, issue.5, pp.745-756, 2016.
DOI : 10.1112/blms/bdw039

URL : http://arxiv.org/pdf/1507.04713

N. Istrati, A characterisation of toric LCK manifolds, J. Symplectic Geom, vol.55, 2017.

N. Istrati and A. Otiman, De Rham and twisted cohomology of Oeljeklaus-Toma manifolds, p.67, 2017.

P. Jahnke and I. Radloff, Projective Threefolds with Holomorphic Conformal Structure, vol.16, pp.595-607, 2005.

Y. Kamishima and L. Ornea, Geometric flow on compact locally conformally Kähler manifolds, Tôhoku Math. J, vol.37, issue.2, p.44, 2005.

Y. Karshon and E. Lerman, Non-Compact Symplectic Toric Manifolds, vol.11, 2015.

. Ma and . Kato, Topology of Hopf surfaces, J. Math. Soc. Japan, vol.27, p.31, 1975.

H. Kasuya, Vaisman metrics on solvmanifolds and Oeljeklaus-Toma manifolds, vol.45, pp.15-26, 2013.

H. Kasuya, Minimal models, formality, and hard Lefschetz properties of solvmanifolds with local systems, J. Differential Geom, vol.93, issue.2, pp.269-297, 2013.

S. Kobayashi and T. Ochiai, Holomorphic structures modeled after hyperquadrics, Tôhoku Math. J, vol.1, issue.2, pp.587-629, 1982.

K. Kodaira, On the Structure of Compact Complex Analytic Surfaces, I,II, American J. Math, vol.88, p.31, 1966.

M. Kourganoff, Transverse similarity structures on foliations, and De Rham decomposition, vol.38, p.51, 2015.

C. R. Lebrun, Anti-self-dual Hermitian metrics on blown-up Hopf surfaces, Math. Ann, vol.289, pp.383-392, 1991.

M. De-león, B. López, J. C. Marrero, and E. Padrón, On the computation of the Lichnerowicz-Jacobi cohomology, J. Geom. Phys, vol.44, issue.4, pp.507-522, 2003.

E. Lerman, Contact Toric Manifolds, vol.1, pp.785-828, 2003.

F. Madani, A. Moroianu, and M. Pilca, Conformally related Kähler metrics and the holonomy of LCK manifolds, to appear in J, Eur. Math. Soc, vol.38

F. Madani, A. Moroianu, and M. Pilca, On Toric Locally Conformally Kähler Manifolds, vol.51, p.58, 2017.

D. Martelli, J. Sparks, and S. Yau, The geometric dual of a-maximisation for toric Sasaki-Einstein manifolds, Comm. Math. Phys, vol.268, pp.39-65, 2006.

A. Moroianu, Lectures on Kähler Geometry, vol.69, 2007.

A. Moroianu and S. Moroianu, On Pluricanonical Locally Conformally Kähler manifolds, IMRN, vol.14, pp.4398-4405, 2017.

A. Moroianu, S. Moroianu, and L. Ornea, Locally conformally Kähler manifolds with holomorphic Lee field, 2017.
DOI : 10.1016/j.difgeo.2018.05.004

URL : http://arxiv.org/pdf/1712.05821

A. Moroianu and L. Ornea, Transformations of locally conformally Kähler manifolds, Manuscripta Math, vol.130, pp.93-100, 2009.

A. Moroianu, M. Pilca, and U. Semmelmann, Homogeneous almost quaternion-Hermitian manifolds, Math. Ann, vol.357, pp.1205-1216, 2013.
DOI : 10.1007/s00208-013-0934-1

URL : https://hal.archives-ouvertes.fr/hal-02102590

S. P. Novikov, Multi-valued functions and functionals. An analogue of Morse theory, Soviet Math. Doklady, vol.24, pp.222-226, 1981.

S. P. Novikov, The Hamiltonian formalism and a multi-valued analogue of Morse theory, Russian Math. Surveys, vol.37, pp.1-56, 1982.

K. Oeljeklaus and M. Toma, Non-Kähler compact complex manifolds associated to number fields, Ann. Inst. Fourier, vol.55, 2005.

K. Oguiso and S. Schröer, Enriques manifolds, J. Reine Angew. Math, vol.661, p.13, 2011.

L. Ornea, M. Parton, and V. Vuletescu, Holomorphic submersions of locally conformally Kähler manifolds, Annali di Matematica, vol.193, p.49, 2014.

L. Ornea and M. Verbitsky, Locally conformal Kähler manifolds with potential, Math. Ann, vol.248, pp.25-33, 2010.

L. Ornea and M. Verbitsky, Oeljeklaus-Toma manifolds admitting no complex subvarieties, Math. Res. Lett, vol.18, issue.4, pp.747-754, 2011.

L. Ornea and M. Verbitsky, Automorphisms of locally conformally Kähler manifolds, Int. Math. Res. Not, vol.2012, issue.4, pp.894-903, 2012.

L. Ornea and M. Verbitsky, Positivity of LCK potential, vol.25, p.37, 2017.

L. Ornea, M. Verbitsky, and V. Vuletescu, Blow-ups of locally conformally Kähler manifolds, Int. Math. Res. Not, vol.12, pp.2809-2821, 2013.

A. Otiman, Locally Conformally Symplectic Bundles, 2015.

A. Otiman, Morse-Novikov cohomology of locally conformally Kähler surfaces, Z, vol.35, p.70

M. Parton and V. Vuletescu, Examples of non-trivial rank in locally conformal Kähler geometry, Math. Z, vol.270, issue.1, pp.179-187, 2012.

M. Pilca, Toric Vaisman Manifolds, J. Geom. Phys, vol.107, pp.149-161, 2016.

M. Pontecorvo, On a question of Vaisman concerning complex surfaces, M. Annali di Matematica, vol.193, pp.1283-1293, 2014.

V. Tosatti, Non-Kähler Calabi-Yau manifolds, Contemp. Math, vol.644, pp.261-277, 2015.

F. Tricerri, Some examples of locally conformal Kähler manifolds, Rend. Sem. Mat. Univers. Politecn. Torino, vol.40, p.34, 1982.

K. Tsukada, Holomorphic forms and holomorphic vector fields on compact generalized Hopf manifolds, Compositio Math, vol.93, pp.1-22, 1994.

K. Tsukada, Holomorphic Maps of Compact Generalized Hopf Manifolds, Geometriae Dedicata, vol.68, pp.61-71, 1997.

K. Tsukada, The canonical foliation of a compact generalized Hopf manifold, Differential Geom. Appl, vol.11, p.37, 1999.

I. Vaisman, On locally conformal almost Kahler manifolds, Israel J. Math, vol.24, pp.338-351, 1976.
DOI : 10.1007/bf02834764

URL : http://dml.cz/bitstream/handle/10338.dmlcz/128246/CzechMathJ_58-2008-1_5.pdf

I. Vaisman, On Locally and Globally Conformal Kähler Manifolds, vol.262, p.37, 1980.
DOI : 10.2307/1999844

I. Vaisman, Generalized Hopf Manifolds, Geometriae Dedicata, vol.13, pp.231-255, 1982.

I. Vaisman, Locally Conformal Symplectic Manifolds, vol.3, p.56, 1985.
DOI : 10.1155/s0161171285000564

URL : https://doi.org/10.1155/s0161171285000564

M. S. Verbitsky, Theorems on the vanishing of cohomology for locally conformally hyperKähler manifolds, vol.246, 2004.

S. Metody and . Prilozh, 64-91, Proc. Steklov Inst. Math, vol.246, pp.54-78, 2004.

V. Vuletescu, Blowing-up points on l.c.K. manifolds, Bull. Math. Soc. Sci. Math. Roumanie (N. S.), vol.52, issue.100, pp.387-390, 2009.

V. Vuletescu, LCK metrics on elliptic principal bundles, p.47, 2010.

V. Vuletescu, LCK metrics on Oeljeklaus-Toma manifolds vs Kronecker's theorem, Bull. Math. Soc. Sci. Math. Roumanie (N. S.), vol.57, issue.105, pp.225-231, 2014.