Chen inequalities on spacelike hypersurfaces of a GRW spacetime

Poyraz N.

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, cilt.81, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 81
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1016/j.difgeo.2022.101863
  • Dergi Adı: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Anahtar Kelimeler: Spacelike hypersurface, Chen inequality, Chen-Ricci inequality, spacetimes, Generalized Robertson-Walker, LIGHT-LIKE HYPERSURFACES, SCALAR CURVATURE, SHAPE OPERATOR, MEAN-CURVATURE, SUBMANIFOLDS
  • Çukurova Üniversitesi Adresli: Evet

Özet

In this paper, we establish Chen-Ricci inequality and Chen inequalities for spacelike hypersurfaces in GRW spacetimes. Considering these inequalities, we give some characterizations. Equality cases are also considered. We show that M is a totally geodesic or a totally umbilical in case of equalities. Moreover, we find some basic inequalities for shape operator of such hypersurfaces and obtain some inequalities for spacelike slices in GRW spacetimes.(c) 2022 Elsevier B.V. All rights reserved.