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2005 | 3 | 2 | 318-330
Tytuł artykułu

On almost cosymplectic (−1, μ, 0)-spaces

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EN
Abstrakty
EN
In our previous paper, almost cosymplectic (κ, μ, ν)-spaces were defined as the almost cosymplectic manifolds whose structure tensor fields satisfy a certain special curvature condition. Amongst other results, it was proved there that any almost cosymplectic (κ, μ, ν)-space can be $$\mathcal{D}$$ -homothetically deformed to an almost cosymplectic −1, μ′, 0)-space. In the present paper, a complete local description of almost cosymplectic (−1, μ, 0)-speces is established: “models” of such spaces are constructed, and it is noted that a given almost cosymplectic (−1, μ 0)-space is locally isomorphic to a corresponding model. In the case when μ is constant, the models can be constructed on the whole of ℝ2n+1 and it is shown that they are left invariant with respect to Lie group actions.
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
2
Strony
318-330
Opis fizyczny
Daty
wydano
2005-06-01
online
2005-06-01
Twórcy
autor
Bibliografia
  • [1] D.E. Blair: Riemannian geometry of contact and symplectic manifolds, Progress in Math., Vol. 203, Birkhäuser, Boston, 2001.
  • [2] D.E. Blair, T. Koufogiorgos and B.J. Papantoniou: “Contact metric manifolds satisfying a nullity condition”, Israel. J. Math., Vol. 91, (1995), pp. 189–214.
  • [3] E. Boeckx: “A full classification of contact metric (κ, μ)-spaces”, Ill. J. Math., Vol. 44, (2000), pp. 212–219.
  • [4] D. Chinea, M. de León and J.C. Marrero: “Stability of invariant foliations on almost contact manifolds”, Publ. Math. Debrecen, Vol. 43, (1993), pp. 41–52.
  • [5] D. Chinea and C. Gonzáles: An example of an almost cosymplectic homogeneous manifold, Lec. Notes Math., Vol. 1209, Springer, Berlin, 1986, pp. 133–142.
  • [6] L.A. Cordero, M. Fernández and M. De León: “Examples of compact almost contact manifolds admitting neither Sasakian nor cosymplectic structures”, Atti Sem. Mat. Fis. Univ. Modena, Vol. 34, (1985–86) pp. 43–54.
  • [7] P. Dacko: “On almost cosymplectic manifolds with the structure vector field ξ belonging to the k-nullity distribution”, Balkan. J. Geom. Appl., Vol. 5(2), (2000), pp. 47–60.
  • [8] P. Dacko and Z. Olszak: “On conformally flat almost cosymplectic manifolds with Kählerian leaves”, Rend. Sem. Mat. Univ. Pol. Torino, Vol. 56, (1998), pp. 89–103.
  • [9] P. Dacko and Z. Olszak: “On almost cosymplectic (κ, μ, ν)-spaces”, in print.
  • [10] H. Endo: “On some properties of almost cosymplectic manifolds”, An. §tiint. Univ. “Al. I. Cuza” Ia§i, Mat., Vol. 42, (1996), pp. 79–94.
  • [11] H. Endo: “On some invariant submanifolds in certain almost cosymplectic manifolds”, An. §tiint. Univ. “Al. I. Cuza” Ia§i, Mat., Vol. 43, (1997), pp. 383–395.
  • [12] H. Endo: “Non-existence of almost cosymplectic manifolds satisfying a certain condition”, Tensor N. S., Vol. 63, (2002), pp. 272–284.
  • [13] S.I. Goldberg and K. Yano: “Integrability of almost cosymplectic structure”, Pacific J. Math., Vol. 31, (1969), pp. 373–382.
  • [14] Z. Olszak: “On almost cosymplectic manifolds”, Kodai Math. J., Vol. 4, (1981), pp. 239–250. http://dx.doi.org/10.2996/kmj/1138036371
  • [15] Z. Olszak: “Curvature properties of quasi-Sasakian manifolds”, Tensor N.S., Vol. 38, (1982), pp. 19–28.
  • [16] Z. Olszak: “Almost cosymplectic manifolds with Kählerian leaves”, Tensor N.S., Vol. 46, (1987), pp. 117–124.
  • [17] S. Tanno: “Ricci curvatures of contact Riemannian manifolds”, Tôhoku Math. J., Vol. 40, (1988), pp. 441–448.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02479207
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