On generalized recurrent Riemannian manifolds

Arslan, KADRİ; De, U.; Murathan, CENGİZHAN; Yildiz, A.

doi:10.1007/s10474-008-8049-y

On generalized recurrent Riemannian manifolds

Arslan K., De U. C., Murathan C., Yildiz A.

ACTA MATHEMATICA HUNGARICA, cilt.123, sa.1-2, ss.27-39, 2009 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 123 Sayı: 1-2
Basım Tarihi: 2009
Doi Numarası: 10.1007/s10474-008-8049-y
Dergi Adı: ACTA MATHEMATICA HUNGARICA
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.27-39
Anahtar Kelimeler: generalized recurrent manifold, concirculary recurent manifold, quasi-Einstein manifold, Ricci-semisymmetry, CLASSIFICATION
Bursa Uludağ Üniversitesi Adresli: Evet

Özet

The object of the present paper is to study a type of Riemannian manifolds called generalized recurrent manifolds. We have constructed two concrete examples of such a manifold whose scalar curvature is non-zero non-constant. Some other properties have been considered. Among others it is shown that on a generalized recurrent manifold with constant scalar curvature, Weyl-semisymmetry and semisymmetry are equivalent. Sufficient condition for a generalized recurrent manifold to be a special quasi Einstein manifold is obtained.