GENERALIZED (κ˜ ≠ −1, µ˜)-PARACONTACT METRIC MANIFOLDS WITH ξ(µ˜) = 0

___

  • [1] Alekseevski, D.V., Cort´es, V., Galaev, A.S. and Leistner, T., Cones over pseudo-Riemannian manifolds and their holonomy, J. Reine Angew. Math. 635 (2009), 23-69.
  • [2] Alekseevski, D.V., Medori, C. and Tomassini, A., Maximally homogeneous para-CR mani- folds, Ann. Glob. Anal. Geom. 30 (2006), 1–27.
  • [3] Bejan, C.L., Almost parahermitian structures on the tangent bundle of an almost para- coHermitian manifold, In: The Proceedings of the Fifth National Seminar of Finsler and Lagrange Spaces (Bra sov, 1988), 105–109, Soc. Stiinte Mat. R. S. Romania, Bucharest, 1989.
  • [4] Buchner, K. and Rosca, R., Vari´etes para-coKählerian ´a champ concirculaire horizontale, C. R. Acad. Sci. Paris 285 (1977), Ser. A, 723–726.
  • [5] Buchner, K. and Rosca, R., Co-isotropic submanifolds of a para-coKa¨hlerian manifold with concicular vector field, J. Geometry 25 (1985), 164–177.
  • [6] Cappelletti Montano, B. and Di Terlizzi, L., Geometric structures associated to a contact metric (κ, µ)-space, Pacific J. Math. 246 no:2 (2010), 257–292.
  • [7] Cappelletti-Montano, B., Kupeli Erken, I. and Murathan, C., Nullity conditions in paracon- tact geometry, Diff. Geom. Appl. 30 (2012), 665–693.
  • [8] Cort´es, V., Mayer, C., Mohaupt, T. and Saueressing, F., Special geometry of Euclidean supersymmetry, 1. Vector multiplets. J. High Energy Phys. (2004) 03:028: 73.
  • [9] Cort´es, V., Lawn, M.A. and Sch¨afer, L., Affine hyperspheres associated to special para-Ka¨hler manifolds, Int. J. Geom. Methods Mod. Phys. 3 (2006), 995–1009.
  • [10] Dacko, P., On almost para-cosymplectic manifolds, Tsukuba J. Math. 28 (2004), 193–213. [11] Kaneyuki, S. and Williams, F. L., Almost paracontact and parahodge structures on manifolds, Nagoya Math. J. 99 (1985), 173–187.
  • [12] Koufogiorgos, T. and Tsichlias, C., On the existence of a new class of contact metric manifolds, Canad. Math. Bull. Vol 43 (2000), 440-447.
  • [13] Koufogiorgos, T. and Tsichlias, C., Generalized (κ, µ)-contact metric manifolds with lgrad κl =constant, J. Geom. 78 (2003), 83-91.
  • [14] Koufogiorgos, T. and Tsichlias, C., Generalized (κ, µ)-contact metric manifolds with ξ(µ) = 0, Tokyo J. Math. Vol 31 (2008), 39-57.
  • [15] Kupeli Erken, I. and Murathan, C., A Complete Study of Three-Dimensional Paracontact (κ, µ, ν)-spaces, Submitted. Available in Arxiv:1305.1511 [math. DG].
  • [16] O’Neill, B., Semi-Riemann Geometry, Academic Press. New York, 1983.
  • [17] Rosca, R. and Vanhecke, L., Su´r une vari´et´e presque paracokähl´erienne munie d’une con- nexion self-orthogonale involutive, Ann. Sti. Univ. “Al. I. Cuza” Ia si 22 (1976), 49–58.
  • [18] Welyczko, J., On basic curvature identities for almost (para)contact metric manifolds. Avail- able in Arxiv: 1209.4731v1 [math. DG].
  • [19] Zamkovoy, S., Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom. 36 (2009), 37–60.