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

• Autorzy: Yulian T. Tsankov
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 53B20: Local Riemannian geometry
• 53B21: Methods of Riemannian geometry

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2005
• Tom: 69
• Numer: 1
• Strony: 205-209

Daty

wydano

2005

Twórcy

autor

Yulian T. Tsankov

• Department of Geometry, Faculty of Mathematics and Informatics, Sofia University "St. Kliment Ohridski", Blvd. "J. Bourchier", 5, 1164 Sofia, Bulgaria

Identyfikatory

DOI

10.4064/bc69-0-16