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We study pseudo symmetric (briefly (PS)n) and pseudo Ricci symmetric (briefly (PRS)n) warped product manifolds M ×F N. If M is (PS)n, then we give a condition on the warping function that M is a pseudosymmetric space and N is a space of constant curvature. If M is (PRS)n, then we show that (i) N is Ricci symmetric and (ii) M is (PRS)n if and only if the tensor T defined by (2.6) satisfies a certain condition.
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참고문헌 (15)
참고문헌 신청
A. G. Walker / 1950 / On Ruse’s spaces of recurrent curvature / Proc. London Math. Soc. (2) 52 : 36 ~ 64
A. Gebarowski / 1992 / Nearly conformally symmetric warped product manifolds / Bull. Inst. Math. Acad. 20 (4) : 359 ~ 377
B. O’Neill / 1983 / Semi-Riemannian Geometry with Applications to the Relativity / Academic Press
E. Cartan / 1926 / Sur une classe remarquable d’espaces de Riemann / Bull. Soc. Math. 54 : 214 ~ 264
G. Soos / 1958 / ¨ Uber die geod¨atischen Abbildungen von Riemannschen R¨aumen auf projektivsymmetrische Riemannsche R¨aume / Acta Math. Acad. Sci. 9 : 359 ~ 361
A. Gebarowski / 1992 / Nearly conformally symmetric warped product manifolds / Bull. Inst. Math. Acad. 20 (4) : 359 ~ 377
B. O’Neill / 1983 / Semi-Riemannian Geometry with Applications to the Relativity / Academic Press
E. Cartan / 1926 / Sur une classe remarquable d’espaces de Riemann / Bull. Soc. Math. 54 : 214 ~ 264
G. Soos / 1958 / ¨ Uber die geod¨atischen Abbildungen von Riemannschen R¨aumen auf projektivsymmetrische Riemannsche R¨aume / Acta Math. Acad. Sci. 9 : 359 ~ 361
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