A Remark on the Axiom of Spheres with Lightlike Submanifolds and Application of Jacobi Equation

作者：Jamali Mohammed^*; Jun Jae Ok; Shahid Mohammad Hasan; Ahmad Mobin

来源：Bulletin of the Malaysian Mathematical Sciences Society, 2014, 37(2): 565-574.

• r-submanifolds
• lightlike submanifolds
• tidal force operator
• Jacobi vector field

In this paper we improve the axiom of r-planes(r-spheres) for lightlike submanifolds given by Kumar, Rani and Nagaich. Moreover we introduce another axiom called axiom of r-submanifolds. We prove that if a lightlike submanifold (M,g,S(TM),S(TM perpendicular to)) of a semi-Riemannian manifold ((M) over bar, (g) over bar) satisfies axiom of r-submanifolds, then it is a real space form. We also use Jacobi equation and obtain some related results to totally umbilical lightlilce submanifold of semi-Riemannian manifold.

• 出版日期2014