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A characterization of n-dimensional hypersurfaces in $R^{n+1}$ with commuting curvature operators

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Tsankov Y.

Banach Center Publications

2005

tom 69

nr 1

205-209

Let Mⁿ be a hypersurface in $R^{n+1}$. We prove that two classical Jacobi curvature operators $J_x$ and $J_y$ commute on Mⁿ, n > 2, for all orthonormal pairs (x,y) and for all points p ∈ M if and only if Mⁿ is a space of constant sectional curvature. Also we consider all hypersurfaces with n ≥ 4 satisfying the commutation relation $(K_{x,y} ∘ K_{z,u})(u) = (K_{z,u} ∘ K_{x,y})(u)$, where $K_{x,y}(u) = R(x,y,u)$, for all orthonormal tangent vectors x,y,z,w and for all points p ∈ M.

Ograniczanie wyników

1 Banach Center Publications

1 Tsankov Y.

1 2005

Wyniki wyszukiwania

A characterization of n-dimensional hypersurfaces in $R^{n+1}$ with commuting curvature operators