Chen–Ricci inequalities for submanifolds of Riemannian and Kaehlerian product manifolds
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Dosyalar
Tarih
2016
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Annales Polonici Mathematici
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Some examples of slant submanifolds of almost product Riemannian manifolds are presented. The existence of a useful orthonormal basis in proper slant submanifolds of a Riemannian product manifold is proved. The sectional curvature, the Ricci curvature and the scalar curvature of submanifolds of locally product manifolds of almost constant curvature are obtained. Chen–Ricci inequalities involving the Ricci tensor and the squared mean curvature for submanifolds of locally product manifolds of almost constant curvature are established. Chen–Ricci inequalities for different kinds of submanifolds of Kaehlerian product manifolds are also given.
Açıklama
Anahtar Kelimeler
Classification: 53C15, 53C40, 53C42, 53C55. Key words and phrases: Chen–Ricci inequality, almost product Riemannian manifold, Riemannian product manifold, Kaehlerian product manifold, slant submanifold.
