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Zbl 1135.53319
Munteanu, M.-I.
A note on doubly warped product contact CR-submanifolds in trans-Sasakian manifolds. (English)
[J] Acta Math. Hung. 116, No. 1-2, 121-126 (2007). ISSN 0236-5294; ISSN 1588-2632/e

Summary: Warped product $CR$-submanifolds in Kählerian manifolds were intensively studied only since 2001 after the impulse given by {\it B. Y. Chen} [Monatsh. Math. 133, 177-195 (2001; Zbl 0996.53044)], [Monatsh. Math. 134, 103--119 (2002; Zbl 0996.53045)]. Immediately after, another line of research, similar to that concerning Sasakian geometry as the odd dimensional version of Kählerian geometry, was developed, namely warped product contact $CR$-submanifolds in Sasakian manifolds cf. {\it I. Mihai} [Geom. Dedicata 109, 165--173 (2004; Zbl 1114.53052)], {\it M. I. Munteanu} [Publ. Math. Debrecen 66, 75--120 (2005; Zbl 1063.53052)]. In this note we prove that there exists no proper doubly warped product contact $CR$-submanifolds in trans-Sasakian manifolds.

MSC 2000:: *53C25 Special Riemannian manifolds
53C40 Submanifolds (differential geometry)

Keywords: trans-Sasakian manifolds; Sasakian manifolds; Kenmotsu manifolds; doubly warped product; contact CR-submanifolds

Citations: Zbl 0996.53044; Zbl 0996.53045; Zbl 1114.53052; Zbl 1063.53052

Cited in: Zbl 1224.53064 Zbl 1180.53058

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