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On weakly and pseudo concircular symmetric structures on a Riemannian manifold. (English) Zbl 1184.53022
The authors study the notions of weakly concircular symmetric and pseudo concircular symmetric Riemannian manifolds which extends the concepts of weakly symmetric and pseudo symmetric Riemannian manifolds considered by L. Tamassy, T. Binh and M.C. Chaki. Totally umbilical and totally geodesic hypersurfaces of these special spaces are characterized. Also an example of a weakly concircular symmetric Riemann manifold is given.

MSC:
53B20Local Riemannian geometry
53B15Other connections
WorldCat.org
Full Text: EuDML
References:
[1] Tamassy L., Binh T. Q.: On weakly symmetric and weakly pseudo projective symmetric Riemannian manifolds. Coll. Math. Soc. J. Bolyai 50 (1989), 663-670. · Zbl 0791.53021
[2] Chaki M. C., Mondal S. P.: On generalised pseudo symmetric manifolds. Publ. Math. Debrecen 51, 1-2 (1997), 35-42. · Zbl 0889.53015
[3] De U. C., Bandyopadhyay: On weakly symmetric Riemannian spaces. Publ. Math. Debrecen 54 (1999), 377-381. · Zbl 0922.53018
[4] Ozen F., Altay S.: On weakly concircular symmetric spaces. Math. Pannonica 16, 1 (2005), 29-38. · Zbl 1082.53021 · eudml:225294
[5] Desa P., Amur K.: On w-recurrent spaces. Tensor 29 (1975), 98-102. · Zbl 0309.53022
[6] Chen B. Y.: Geometry of Submanifolds. : Marcel-Deker, New York. 1973. · Zbl 0262.53036
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