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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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In this paper we study the properties of conformally recur- rent pseudo Riemannian manifolds admitting a proper conformal vector field with respect to the scalar field σ, focusing particularly on the 4- dimensional Lorentzian case. Some general properties already proven by one of the present authors for pseudo conformally symmetric manifolds endowed with a conformal vector field are proven also in the case, and some new others are stated. Moreover interesting results are pointed out; for example, it is proven that the Ricci tensor under certain conditions is Weyl compatible: this notion was recently introduced and investigated by one of the present authors. Further we study conformally recurrent 4-dimensional Lorentzian manifolds (space-times) admitting a conformal vector field: it is proven that the covector σㅎj is null and unique up to scaling; moreover it is shown that the same vector is an eigenvector of the Ricci tensor. Finally, it is stated that such space-time is of Petrov type N with respect to σj.
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[학술지(정
A. Avez / 1962 / Formule de Gauss-Bonnet-Chern en metrique de signature quelconque / C. R. Acad. Sci. Paris 255 : 2049 ~ 2051
A. Derdzinski / 1983 / Codazzi tensor fields, curvature and Pontryagin forms / Proc. London Math. Soc 47 (1) : 15 ~ 26
A. Derdzinski / 2008 / On compact manifolds admitting indefinite metrics with parallel Weyl tensor / J. Geom. Phys 58 (9) : 1137 ~ 1147
A. Z. Petrov / 2000 / The classification of spaces defining gravitational field / Gen. Relativity Gravitation 32 (8) : 1665 ~ 1685
A. Avez / 1962 / Formule de Gauss-Bonnet-Chern en metrique de signature quelconque / C. R. Acad. Sci. Paris 255 : 2049 ~ 2051
A. Derdzinski / 1983 / Codazzi tensor fields, curvature and Pontryagin forms / Proc. London Math. Soc 47 (1) : 15 ~ 26
A. Derdzinski / 2008 / On compact manifolds admitting indefinite metrics with parallel Weyl tensor / J. Geom. Phys 58 (9) : 1137 ~ 1147
A. Z. Petrov / 2000 / The classification of spaces defining gravitational field / Gen. Relativity Gravitation 32 (8) : 1665 ~ 1685
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