ON GENERALIZED RICCI-RECURRENT TRANS-SASAKIAN MANIFOLDS

Generalized Ricci-recurrent trans-Sasakian manifolds are studied. Among others, it is proved that a generalized Ricci-recurrent cosymplectic manifold is always recurrent Generalized Ricci-recurrent trans-Sasakian manifolds of dimension $\geq$ 5 are locally classified. It is also proved that if M is...

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Bibliographic Details
Published inJournal of the Korean Mathematical Society Vol. 39; no. 6; pp. 953 - 961
Main Authors Kim, Jeong-Sik, Prasad, Rajendra, Tripathi, Mukut-Mani
Format Journal Article
LanguageKorean
Published 대한수학회 01.11.2002
Subjects
수학
{\beta}$-Kenmotsu
Sasakian
{\alpha}$-Sasakian
Kenmotsu
f-Kenmotsu
cosymplectic and trans-Sasakian structures
Ricci-recurrent
generalized Ricci-recurrent and Einstein manifolds
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Summary:Generalized Ricci-recurrent trans-Sasakian manifolds are studied. Among others, it is proved that a generalized Ricci-recurrent cosymplectic manifold is always recurrent Generalized Ricci-recurrent trans-Sasakian manifolds of dimension $\geq$ 5 are locally classified. It is also proved that if M is one of Sasakian, $\alpha$-Sasakian, Kenmotsu or $\beta$-Kenmotsu manifolds, which is gener-alized Ricci-recurrent with cyclic Ricci tensor and non-zero A (ξ) everywhere; then M is an Einstein manifold.
Bibliography:KISTI1.1003/JNL.JAKO200211921408331
G704-000208.2002.39.6.003
ISSN:0304-9914
2234-3008