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2005 | 3 | 2 | 309-317
Tytuł artykułu

On the bochner conformal curvature of Kähler-Norden manifolds

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Języki publikacji
EN
Abstrakty
EN
Using the one-to-one correspondence between Kähler-Norden and holomorphic Riemannian metrics, important relations between various Riemannian invariants of manifolds endowed with such metrics were established in my previous paper [19]. In the presented paper, we prove that there is a strict relation between the holomorphic Weyl and Bochner conformal curvature tensors and similarly their covariant derivatives are strictly related. Especially, we find necessary and sufficient conditions for the holomorphic Weyl conformal curvature tensor of a Kähler-Norden manifold to be holomorphically recurrent.
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
2
Strony
309-317
Opis fizyczny
Daty
wydano
2005-06-01
online
2005-06-01
Twórcy
Bibliografia
  • [1] A. Borowiec, M. Ferraris, M. Francaviglia and I. Volovich: “Almost-complex and almost-product Einstein manifolds from a variational principle”, J. Math. Physics, Vol. 40(7), (1999), pp. 3446–3464. http://dx.doi.org/10.1063/1.532899
  • [2] A. Borowiec, M. Francaviglia and I. Volovich: “Anti-Kählerian manifolds”, Diff. Geom. Appl., Vol. 12, (2000), pp. 281–289. http://dx.doi.org/10.1016/S0926-2245(00)00017-6
  • [3] E.J. Flaherty, Jr.: “The nonlinear gravitation in interaction with a photon”, General Relativity and Gravitation, Vol. 9(11), (1978), pp. 961–978. http://dx.doi.org/10.1007/BF00784657
  • [4] A. Derdziński: “On homogeneous conformally symmetric pseudo-Riemannian manifolds”, Colloq. Math., Vol. 40, (1978), pp. 167–185.
  • [5] A. Derdziński: “The local structure of essentially conformally symmetric manifolds with constant fundamental function, I. The elliptic case, II. The hyperbolic case, III. The parabolic case”, Colloq. Math., Vol. 42, (1979), pp. 59–81; Vol. 44, (1981), pp. 77–95; Vol. 44, (1981), pp. 249–262.
  • [6] G.T. Ganchev and A.V. Borisov: “Note on the almost complex manifolds with Norden metric”, Compt. Rend. Acad. Bulg. Sci., Vol. 39, (1986), pp. 31–34.
  • [7] G.T. Ganchev, K. Gribachev and V. Mihova: “B-connections and their conformal invariants on conformally Kaehler manifolds with B-metric”, Publ. Inst. Math., Vol. 42(56), (1987), pp. 107–121.
  • [8] G. Ganchev and S. Ivanov: “Connections and curvatures on complex Riemannian manifolds”, Internal Report, No. IC/91/41, International Centre for Theoretical Physics, Trieste, Italy, 1991.
  • [9] G.T. Ganchev and S. Ivanov: “Characteristic curvatures on complex Riemannian manifolds”, Riv. Math. Univ. Parma (5), Vol. 1, (1992), pp. 155–162.
  • [10] S. Ivanov: “Holomorphically projective transformations on complex Riemannian manifold”, J. Geom., Vol. 49, (1994), pp. 106–116. http://dx.doi.org/10.1007/BF01228055
  • [11] S. Kobayashi and K. Nomizu: Foundations of differential geometry, Vol. I, II, Interscience Publishers, New York, 1963, 1969.
  • [12] C.R. LeBrun: “H-space with a cosmological constant”, Proc. Roy. Soc. London, Ser. A, Vol. 380, (1982), pp. 171–185. http://dx.doi.org/10.1098/rspa.1982.0035
  • [13] C. LeBrun: “Spaces of complex null geodesics in complex-Riemannian geometry”, Trans. Amer. Math. Soc., Vol. 278, (1983), pp. 209–231. http://dx.doi.org/10.2307/1999312
  • [14] Z. Olszak: “On conformally recurrent manifolds, II. Riemann extensions”, Tensor N.S., Vol. 49, (1990), pp. 24–31.
  • [15] W. Roter: “On a class of conformally recurrent manifolds”, Tensor N.S., Vol. 39, (1982), pp. 207–217.
  • [16] W. Roter: “On the existence of certain conformally recurrent metrics”, Colloq. Math., Vol. 51, (1987), pp. 315–327.
  • [17] K. Sluka: “On Kähler manifolds with Norden metrics”, An. Stiint. Univ. “Al.I. Cuza” Ia§i, Ser. Ia Mat., Vol. 47 (2001), pp. 105–122.
  • [18] K. Sluka: “Properties of the Weyl conformal curvature of Kähler-Norden manifolds”, In: Steps in Differental Geometry (Proc. Colloq. Diff. Geom. July 25–30, 2000), Debrecen, 2001, pp. 317–328.
  • [19] K. Sluka: “On the curvature of Kähler-Norden manifolds”, J. Geom. Physics, (2004), in print.
  • [20] Y.C. Wong: “Linear connexions with zero torsion and recurrent curvature”, Trans. Amer. Math. Soc., Vol. 102, (1962), pp. 471–506. http://dx.doi.org/10.2307/1993618
  • [21] N. Woodhouse: “The real geometry of complex space-times”, Int. J. Theor. Phys., Vol. 16, (1977), pp. 663–670. http://dx.doi.org/10.1007/BF01812224
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02479206
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