Immersions of Lorentzian submanifolds into R1m with pointwise 2-planar sections and on the circles and pseudo spheres in Lorentzian geometry

E Özdamar,C Murathan

doi:10.1501/commua1_0000000473

Abstract

Immersions of Lorentzian submanifolds into R1m with pointwise 2-planar sections and on the circles and pseudo spheres in Lorentzian geometry

Highlights

We have taken the references [1], [2] and [4] as a base even uotations, used here.Let Rf be standart semi-Riemannian manifold that j denotes the index of RjTM. y and y stand for the connections on Rj“ and Mı®, respectively, where Mı® c RjTM and Mı® is a submanifold of Rj“ and has index i
For every vector fields X, Y tauget to Mj® and normal to Mı®, that is, X, Y e y (Mı®) Ç / e (M)ı®.b, .^here D denotes the normal connection on Mı®
By a Carton frame {T, Y, Z) of a null curve a we mean a family of veetor fields T, Y, Z along « satisfying the following çonditions a'(s) = 'T, g (T; T) g(Y, Y)=0 g(T,Y) -1, g (T, Z) = g (Y, Z) = 0, g (Z, Z) = 1

Summary

Introduction

We have taken the references [1], [2] and [4] as a base even uotations, used here.Let Rf be standart semi-Riemannian manifold that j denotes the index of RjTM. y and y stand for the connections on Rj“ and Mı®, respectively, where Mı® c RjTM and Mı® is a submanifold of Rj“ and has index i. By a Carton frame {T, Y, Z) of a null curve a we mean a family of veetor fields T, Y, Z along « satisfying the following çonditions a'(s) = 'T, g (T; T) g(Y, Y)=0 g(T,Y) -1, g (T, Z) = g (Y, Z) = 0, g (Z, Z) = 1 R: If the curve s — y(s) time-like circle y satisfies the following third order differential equation.

Results

Conclusion