Ouyang Chong-zhen
Abstract
Let x:Mn→En+1 be an orientable hypersurface immersed into the Euclidean space.The map =xxt(t denot transpose) is called the quadric representation of Mn.It studies the hypersurface in En+1 which satisfy □=B+C,where □ is the linearized operator of the mean curvature of hypersurface,B and C are two constant matrices.
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Let x:Mn→En+1 be an orientable hypersurface immersed into the Euclidean space.The map =xxt(t denot transpose) is called the quadric representation of Mn.It studies the hypersurface in En+1 which satisfy □=B+C,where □ is the linearized operator of the mean curvature of hypersurface,B and C are two constant matrices.
Key concepts: Hypersurface, Quadric, Transpose, Mathematics, Euclidean geometry, Mean curvature, Constant (computer programming), Pure mathematics