On a class Riemannian manifolds with harmonic Weyl conformal curvature tensor
Abstract
The paper deals with the local structure of those n-dimensional (n ≥ 5) Riemannian manifolds of harmonic conformal curvature which are not conformally flat and admit a non-homothetic conformal change of metric such that the transformed metric is locally symmetric.
References
A.L. Besse, Einstein Manifolds, Springer-Verlag, Berlin – Heidelberg – New York – London – Paris – Tokyo, 1987.
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M.C. Chaki, B. Gupta, On conformally symmetric spaces, Indian J. of Math. 5 (1963), 113-122.
##plugins.generic.googleScholarLinks.settings.viewInGS##
J. Deprez, W. Roter, L. Verstraelen, Conditions on the projective curvature tensor of conformally flat Riemannian manifolds, Kyungpook Math. J. 29(2) (1989), 153-166.
##plugins.generic.googleScholarLinks.settings.viewInGS##
A. Derdziński, W. Roter, On conformally symmetric manifolds with metrics of indices 0 and 1, Tensor N.S. 31 (1977), 255-259.
##plugins.generic.googleScholarLinks.settings.viewInGS##
A. Derdziński, W. Roter, Some theorems on conformally symmetric manifolds, Tensor N.S. 32 (1978), 11-23.
##plugins.generic.googleScholarLinks.settings.viewInGS##
L.P. Eisenhart, Riemannian Geometry, 2nd edition, Princeton University Press, Princeton 1949.
##plugins.generic.googleScholarLinks.settings.viewInGS##
W. Grycak, On generalized curvature tensors and symmetric (0,2)-tensors with a symmetry condition imposed on the second derivative, Tensor N.S. 33 (1979), 150-152.
##plugins.generic.googleScholarLinks.settings.viewInGS##
H.K. Nickerson, On conformally symmetric spaces, Geometria Dedicata 18 (1985), 87-99.
##plugins.generic.googleScholarLinks.settings.viewInGS##
E.M. Patterson, A class of critical Riemannian metrics, J. London Math. Soc. (2), (1981), 349-358.
##plugins.generic.googleScholarLinks.settings.viewInGS##
W. Roter, On a generalization of conformally symmetric metrics, Tensor N.S. 46 (1987), 278-286.
##plugins.generic.googleScholarLinks.settings.viewInGS##
W. Roter, On conformally related conformally recurrent metrics, I. Some general results, Colloq. Math. 47 (1982), 39-46.
##plugins.generic.googleScholarLinks.settings.viewInGS##
J.A. Schouten, Ricci-Calculus, 2nd edition, Springer-Verlag, Berlin – Goettingen – Heidelberg, 1954.
##plugins.generic.googleScholarLinks.settings.viewInGS##
T.Y. Thomas, The decomposition of Riemannian spaces in the large, Monatsh. f. Math. und Physik 47 (1939), 388-418.
##plugins.generic.googleScholarLinks.settings.viewInGS##
