Abstract

Title: On the classification of biconservative submanifolds of codimension 2 in $S^4xR$ and $H^4xR$

Abstract: Biconservative submanifolds arise as the vanishing of the stress-energy tensor associated with the variational problem of biharmonic submanifolds. More precisely, an isometric immersion $\phi : M → N$ between two Riemannian manifolds is biconservative if the tangent component of its bitension field is identically zero. There are few Riemannian manifolds for which biconservative submanifolds are classified. In this talk, I will discuss the complete classification of biconservative submanifolds of co-dimension 2 in $S^4 x R$ and $H^4 x R$ with an additional condition of parallel mean curvature vector field.