Abstract
This is a review paper of the essential research on metric (Killing, homothetic, and conformal) symmetries of Riemannian, semi-Riemannian, and lightlike manifolds. We focus on the main characterization theorems and exhibit the state of art as it now stands. A sketch of the proofs of the most important results is presented together with sufficient references for related results.
Highlights
The measurement of distances in a Euclidean space R3 is represented by the distance element ds[2] dx2 dy[2] dz21.1 with respect to a rectangular coordinate system x, y, z
In 1991, Bejancu and Duggal 5 introduced a general geometric technique to study the extrinsic geometry of degenerate submanifolds, popularly known as lightlike submanifolds of a semi-Riemannian manifold
The purpose of this paper is to present a survey of research done on the geometry and physics of Riemannian, semi-Riemannian, in particular, Lorentzian and lightlike manifolds M, g having a metric symmetry defined by 1.3
Summary
1.1 with respect to a rectangular coordinate system x, y, z. A degenerate submanifold M, g of a semi-Riemannian manifold M, g may not be studied intrinsically since due to the induced degenerate tensor field g on M one cannot use, in general, the geometry of M. To overcome this difficulty, Kupeli used the quotient space TM∗ TM/Rad TM and the canonical projection P : TM → TM∗ for the study of intrinsic geometry of M. In 1991, Bejancu and Duggal 5 introduced a general geometric technique to study the extrinsic geometry of degenerate submanifolds, popularly known as lightlike submanifolds of a semi-Riemannian manifold. For this reason we have provided a large number of references for more related results
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
