scholarly journals Characteristic Lightlike Submanifolds of an IndefiniteS-Manifold

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Jae Won Lee
Keyword(s):  
Vector Fields ◽  
Space Form ◽  
Characteristic Vector ◽  
Indefinite Metric ◽  
Totally Umbilical ◽  
Screen Distribution ◽  
Lightlike Submanifolds ◽  
Characteristic Vector Fields

We study characteristicr-lightlike submanifoldsMtangent to the characteristic vector fields in an indefinite metricS-manifold, and we also discuss the existence of characteristic lightlike submanifolds of an indefiniteS-space form under suitable hypotheses: (1)Mis totally umbilical or (2) its screen distributionS(TM)is totally umbilical inM.

scholarly journals Half lightlike submanifolds of a semi-Riemannian manifold of quasi-constant curvature

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1737-1745
Author(s):  
Dae Jin ◽  
Jae Lee
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Constant Curvature ◽  
Curvature Vector ◽  
Conformal Killing ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Screen Distribution ◽  
Lightlike Submanifolds

We study the geometry of half lightlike submanifolds (M,g,S(TM), S(TM?)) of a semi-Riemannian manifold (M~,g~) of quasi-constant curvature subject to the following conditions; (1) the curvature vector field ? of M~ is tangent to M, (2) the screen distribution S(TM) of M is either totally geodesic or totally umbilical in M, and (3) the co-screen distribution S(TM?) of M is a conformal Killing distribution.

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