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Chen–Ricci inequalities for submanifolds of Riemannian and Kaehlerian product manifolds

Volume 116 / 2016

Erol Kılıç, Mukut Mani Tripathi, Mehmet Gülbahar Annales Polonici Mathematici 116 (2016), 37-56 MSC: 53C15, 53C40, 53C42, 53C55. DOI: 10.4064/ap3666-12-2015 Published online: 4 February 2016

Abstract

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.

Authors

  • Erol KılıçDepartment of Mathematics
    Faculty of Science and Art
    İnönü University
    Malatya, Turkey
    e-mail
  • Mukut Mani TripathiDepartment of Mathematics
    Institute of Science Banaras Hindu University
    Varanasi, India
    e-mail
  • Mehmet GülbaharDepartment of Mathematics
    Faculty of Science and Art
    Siirt University
    Siirt, Turkey
    e-mail

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