Taiwanese Journal of Mathematics


Verónica Martín-Molina

Full-text: Open access


We study non-paraSasakian paracontact metric $(\kappa,\mu)$-spaces with $\kappa=-1$ (equivalent to $h^2=0$ but $h\neq0$). These manifolds, which do not have a contact geometry counterpart, will be classified locally in terms of the rank of $h$. We will also give explicit examples of every possible constant rank of $h$.

Article information

Taiwanese J. Math., Volume 19, Number 1 (2015), 175-191.

First available in Project Euclid: 4 July 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C50: Lorentz manifolds, manifolds with indefinite metrics

paracontact metric manifold paraSasakian nullity distribution $(\kappa, \mu)$-spaces


Martín-Molina, Verónica. PARACONTACT METRIC MANIFOLDS WITHOUT A CONTACT METRIC COUNTERPART. Taiwanese J. Math. 19 (2015), no. 1, 175--191. doi:10.11650/tjm.19.2015.4447. https://projecteuclid.org/euclid.twjm/1499133624

Export citation


  • D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Second Edition, Progress in Mathematics 203, Birkhäuser, Boston, 2010.
  • D. E. Blair, T. Koufogiorgos and B. J. Papantoniou, Contact metric manifolds satisfyng a nullity condition, Israel J. Math., 91 (1995), 189-214.
  • E. Boeckx, A full classification of contact metric $(\kappa,\mu)$-spaces, Illinois J. Math., 44 (2000), 212-219.
  • B. Cappelletti Montano, Bi-Legendrian structures and paracontact geometry, Int. J. Geom. Met. Mod. Phys., 6 (2009), 487-504.
  • B. Cappelletti Montano, Bi-paracontact structures and Legendre foliations, Kodai Math. J., 33 (2010), 473-512.
  • B.\! Cappelletti\! Montano,\! A.\! Carriazo\! and\! V.\! Mart\ptmrín-Molina,\! Sasaki-Einstein\! and\! paraSasaki-Einstein metrics from $(\kappa,\mu)$-structures, J. Geom. Physics., 73 (2013) 20-36.
  • B. Cappelletti Montano and L. Di Terlizzi, Geometric structures associated with a contact metric $(\kappa,\mu)$-space, Pacific J. Math., 246 (2010), 257-292.
  • B. Cappelletti Montano, I. Küpeli Erken and C. Murathan, Nullity conditions in paracontact geometry, Differential Geom. Appl., 30 (2012), 665-693.
  • G. Calvaruso, Homogeneous paracontact metric three-manifolds, Illinois J. Math., 55 (2011), 697-718.
  • G. Calvaruso and D. Perrone, Geometry of $H$-paracontact Metric Manifolds, arXiv:1307. 7662.
  • S. Ivanov, D. Vassilev and S. Zamkovoy, Conformal paracontact curvature and the local flatness theorem, Geom. Dedicata, 144 (2010), 79-100.
  • S. Kaneyuki and F. L. Williams, Almost paracontact and parahodge structures on manifolds, Nagoya Math. J., 99 (1985), 173-187.
  • C. Murathan and I. Küpeli Erken, The Harmonicity of the Reeb Vector Dield on Paracontact Metric $3$-manifolds, arXiv:1305.1511v2.
  • B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.
  • S. Zamkovoy, Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom., 36 (2009), 37-60.
  • S. Zamkovoy and V. Tzanov, Non-existence of flat paracontact metric structures in dimension greater than or equal to five, Annuaire Univ. Sofia Fac. Math. Inform., 100 (2011), 27-34.