Geometry of warped product pointwise semi-slant submanifolds of cosymplectic manifolds and its applications

Ali A., Ozel C.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, cilt.14, sa.3, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 3
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1142/s0219887817500426
  • Dergi Adı: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Warped products, pointwise semi-slant submanifolds, compact Riemannian submanifolds, cosymplectic manifold, cosymplectic space forms, Hamiltonian, kinetic energy, CR-SUBMANIFOLDS, CLASSIFICATION
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

It is known from [K. Yano and M. Kon, Structures on Manifolds ( World Scientific, 1984)] that the integration of the Laplacian of a smooth function defined on a compact orientable Riemannian manifold without boundary vanishes with respect to the volume element. In this paper, we find out the some potential applications of this notion, and study the concept of warped product pointwise semi-slant submanifolds in cosymplectic manifolds as a generalization of contact CR-warped product submanifolds. Then, we prove the existence of warped product pointwise semi-slant submanifolds by their characterizations, and give an example supporting to this idea. Further, we obtain an interesting inequality in terms of the second fundamental form and the scalar curvature using Gauss equation and then, derive some applications of it with considering the equality case. We provide many trivial results for the warped product pointwise semi-slant submanifolds in cosymplectic space forms in various mathematical and physical terms such as Hessian, Hamiltonian and kinetic energy, and generalize the triviality results for contact CR-warped products as well.