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2008 | 6 | 1 | 43-75
Tytuł artykułu

Kähler manifolds of quasi-constant holomorphic sectional curvatures

Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
The Kähler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kähler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the geometric angle, associated with the section. A curvature identity characterizing such manifolds is found. The biconformal group of transformations whose elements transform Kähler metrics into Kähler ones is introduced and biconformal tensor invariants are obtained. This makes it possible to classify the manifolds under consideration locally. The class of locally biconformal flat Kähler metrics is shown to be exactly the class of Kähler metrics whose potential function is only a function of the distance from the origin in ℂn. Finally we show that any rotational even dimensional hypersurface carries locally a natural Kähler structure which is of quasi-constant holomorphic sectional curvatures.
Wydawca
Czasopismo
Rocznik
Tom
6
Numer
1
Strony
43-75
Opis fizyczny
Daty
wydano
2008-03-01
online
2008-02-26
Twórcy
Bibliografia
  • [1] Boju V., Popescu M., Espaces à courbure quasi-constante, J. Differential Geom., 1978, 13, 373–383 (in French)
  • [2] Bryant R., Bochner-Kähler metrics, J. Amer. Math. Soc., 2001, 14, 623–715 http://dx.doi.org/10.1090/S0894-0347-01-00366-6
  • [3] Bishop R., O’Neil B, Manifolds of negative curvature, Trans. Amer. Math. Soc., 1969, 145, 1–49 http://dx.doi.org/10.2307/1995057
  • [4] Gray A., Hervella L., The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura Appl., 1980, 123, 35–58 http://dx.doi.org/10.1007/BF01796539
  • [5] Ganchev G., Mihova V., Riemannian manifolds of quasi-constant sectional curvatures, J. Reine Angew. Math., 2000, 522, 119–141
  • [6] Ganchev G., Mihova V, Kähler metrics generated by functions of the time-like distance in the flat Kähler-Lorentz space, J. Geom. Phys., 2007, 57, 617–640 http://dx.doi.org/10.1016/j.geomphys.2006.05.004
  • [7] Ganchev G, Mihova V., Warped product Kähler manifolds and Bochner-Kähler metrics, preprint available at http://arxiv.org/abs/math/0605082
  • [8] Janssens D., Vanhecke L., Almost contact structures and curvature tensors, Kodai Math. J., 1981, 4, 1–27 http://dx.doi.org/10.2996/kmj/1138036310
  • [9] Kobayashi S., Nomizu K., Foundations of Differential Geometry, Vol. II, Interscience Publishers John Wiley & Sons, New York-London-Sydney, 1969
  • [10] Tashiro Y., On contact structure of hypersurfaces in complex manifolds I, Tôhoku Math. J. (2), 1963, 15, 62–78 http://dx.doi.org/10.2748/tmj/1178243870
  • [11] Tashiro Y., On contact structure of hypersurfaces in complex manifolds II, Tôhoku Math. J. (2), 1963, 15, 167–175 http://dx.doi.org/10.2748/tmj/1178243843
  • [12] Tachibana S., Liu R.C., Notes on Kählerian metrics with vanishing Bochner curvature tensor, Kōdai Math. Sem. Rep., 1970, 22, 313–321 http://dx.doi.org/10.2996/kmj/1138846167
  • [13] Tricerri F., Vanhecke L., Curvature tensors on almost Hermitian manifolds, Trans. Amer. Math. Soc., 1981, 267, 365–397 http://dx.doi.org/10.2307/1998660
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-008-0004-1
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