Proper biconservative immersions into the Euclidean space

By Stefano Montaldo, C. Oniciuc, A. Ratto. 2013

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In this paper, using the framework of equivariant differential geometry, we study proper $$\hbox {SO}(p+1) \times \hbox {SO}(q+1)$$SO(p+1)×SO(q+1)-invariant biconservative hypersurfaces into the Euclidean space $${\mathbb {R}}^n$$Rn ($$n=p+q+2$$n=p+q+2) and proper $$\hbox {SO}(p+1)$$SO(p+1)-invariant biconservative hypersurfaces into the Euclidean space $${\mathbb {R}}^n$$Rn ($$n=p+2$$n=p+2). Moreover, we show that, in these two classes of invariant families, there exists no proper biharmonic immersion.

Subfields: Applied Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ed1079d422351603b954bda5fc8b60578662cfc7