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In this paper, we study some geometric structures of a weakly cyclic $Z$-symmetric manifold (briefly, $[WCZS]_{n}$). More precisely, we prove that a conformally flat $[WCZS]_{n}$ satisfying certain conditions is special conformally flat and hence the manifold can be isometrically immersed in an Euclidean manifold $E^{n+1}$ as a hypersurface if the manifold is simply connected. Also we show that there exists a $[WCZS]_{4}$ with one parameter family of its associated 1-forms.
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참고문헌 (19)
참고문헌 신청
T. Adati / 1967 / On a Riemannian space with recurrent conformal curvature / Tensor (N.S.) 18:348~354
J. K. Beem / 1981 / Global Lorentzian Geometry / Marcel Dekker Inc.
T. Q. Binh / 1989 / On weakly symmetric and weakly projectively symmetric Riemannian manifolds / Colloq. Math. Soc. Janos Bolyai 56:663~670
T. Q. Binh / 1993 / On weakly symmetries of Einstein and Sasakian manifolds / Tensor (N.S.) 53:140~148
E. Cartan / 1926 / Sur une classes remarquable d'espaces de Riemannian / Bull. Soc. Math. France 54:214~264
J. K. Beem / 1981 / Global Lorentzian Geometry / Marcel Dekker Inc.
T. Q. Binh / 1989 / On weakly symmetric and weakly projectively symmetric Riemannian manifolds / Colloq. Math. Soc. Janos Bolyai 56:663~670
T. Q. Binh / 1993 / On weakly symmetries of Einstein and Sasakian manifolds / Tensor (N.S.) 53:140~148
E. Cartan / 1926 / Sur une classes remarquable d'espaces de Riemannian / Bull. Soc. Math. France 54:214~264
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