..., we have the following equations [ 28 ]: Ankit Yadav can be contacted at: ankityadav93156@gmail.com Lightlike submanifolds Totally umbilical lightlike submanifolds Metallic semi-Riemannian manifolds Warped product Primary 53C15 Secondary 53C40 53C50 (2.1) T N...

... and that g₃ is flat. Recently, in [ 11 ] Cakmak, Karakan, Kiziltug and Yoon studied the translation surfaces in three-dimensional Galilean space under the condition. Lorentz Heisenberg space Laplace operator Translation surface Space-like surface 53A10 53C30 53C42 53C50...

... geometry. Due to extensive use as a tool to understand theory of relativity, it becomes a topic of interest for mathematicians and physicists. 53C15 53C40 53C50 Metallic semi-Riemannian manifolds Warped product lightlike submanifolds Irrotational lightlike submanifolds © Gauree...

... umbilic submanifolds Invariant submanifolds Sasakian manifolds Primary 53C25 Secondary 53C40 53C50 Unlike non-degenerate submanifolds, lightlike submanifolds are quite complicated to study. One of the main reasons is that the tangent and normal bundles of a lightlike submanifold have...