On null submanifolds of generalized Robertson–Walker space forms
On null submanifolds of generalized Robertson–Walker space forms
We investigate totally umbilical r -null submanifolds of generalized Robertson–Walker space forms. Usinggeneralized Newton transformations, we obtain new geometric configurations for the mean curvature functions whichgeneralize many well-known results on null geometry.
___
- [1] Albujer AL, Haesen S. A geometrical interpretation of the null sectional curvature. Journal of Geometry and
Physics 2010; 60: 471-476.
- [2] Andrzejewski K, Kozłowski W, Niedziałomski K. Generalized Newton transformation and its applications to
extrinsic geometry. Asian Journal of Mathematics 2016; 20: 293-322.
- [3] Andrzejewski K, Walczak PG. The Newton transformation and new integral formulae for foliated manifolds.
Annals of Global Analysis and Geometry 2010; 3: 103-111.
- [4] Chen BY, Van der Veken J. Spatial and Lorentzian Surfaces in Robertson-Walker space-times. Journal of Mathematical
Physics 2007; 48: 1-12.
- [5] Duggal KL, Bejancu A. Lightlike Subamnifold of Semi-Riemannian Manifolds and Applications. Dordrecht, the
Netherlands: Kluwer Academic Publishers, 1996.
- [6] Duggal KL, Sahin B. Lightlike submanifolds of indefinite Sasakian manifolds. International Journal of Mathematics
and Mathematical Sciences 2007: Art. ID 57585: 21 pp.
- [7] Duggal KL, Sahin B. Differential Geometry of Lightlike Submanifolds, Frontiers in Mathematics. Basel, Switzerland:
Birkhäuser Verlag, 2010.
- [8] Duggal KL, Jin DH. Geometry of null curves. Mathematics Journal of Toyama University 1999; 22: 95-120.
- [9] Duggal KL, Jin DH. Half lightlike submanifolds of codimension 2. Mathematics Journal of Toyama University
1999; 22: 121-161.
- [10] Duggal KL, Jin DH. Totally umbilical lightlike submanifolds. Kodai Mathematical Journal 2003; 26: 49-68.
- [11] Erdogan FE, Güneş R, Şahin B. Half-lightlike submanifolds with planar normal sections in R4
2 . Turkish Journal
of Mathematics 2014; 38: 764-777.
- [12] Gupta RS, Upadhyay A, Shaffuddin A. Lightlike submanifolds of indefinite cosymplectic manifolds. Analele
ştiinţifice ale Universităţii ”Al. I. Cuza” din Iaşi Matematică (NS) 2012; 58: 157-180.
- [13] Kang TH. On Lightlike hypersurfaces of a GRW space-time. Bulletin of the Korean Mathematical Society 2012;
49: 863-874.
- [14] Kang TH. On Lightlike submanifolds of a GRW space-time. Communications of the Korean Mathematical Society
2014; 29: 295-310.
- [15] Kupeli DN. Singular Semi-Riemannian Geometry, Mathematics and Its Applications. Kluwer Academic Publishers,
1996.
- [16] Massamba F. Totally contact umbilical lightlike Hypersurfaces of indefinite Sasakian manifolds. Kodai Mathematical
Journal 2008; 31: 338-358.
- [17] Massamba F. Almost Weyl structures on null geometry in indefinite Kenmotsu manifolds. Mathematica Slovaca
2016; 66: 1443-1458.
- [18] Massamba F. A conformal connection on null hypersurfaces of indefinite Kenmotsu manifolds. Bulletin of the
Malaysian Mathematical Sciences Society 2017; 40: 1559-1575
- [19] Massamba F, Ssekajja S. A New approach to totally umbilical null submanifolds. Novi Sad Journal of Mathematics
2017; 47: 63-76.
- [20] Perktaş SY, Erdogan FE. On generalized CR-lightlike submanifolds. Palestine Journal of Mathematics 2019; 8:
200-208.
- [21] O’Neill B. Semi-Riemannian Geometry, with Applications to Relativity. Pure and Applied Mathematics. Academic
Press, 1983.