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Four-dimensional Riemannian manifolds with commuting higher order Jacobi operators | | Maria Ivanova
; Veselin Videv
; Zhivko Zhelev
; | | Date: |
3 Jan 2007 | | Subject: | Differential Geometry | | Abstract: | We consider four-dimensional Riemannian manifolds with commuting higher order Jacobi operators defined on two-dimensional orthogonal subspaces (polygons) and on their orthogonal subspaces. indent More precisely, we discuss higher order Jacobi operator $mathcal{J}(X)$ and its commuting associated operator $mathcal{J}(X^{perp})$ induced by the orthogonal complement $X^{perp}$ of the vector $X$, i. e. $mathcal{J}(X)circmathcal{J}(X^{perp})=mathcal{J}(X^{perp})circ mathcal{J}(X)$. indent At the end some new central theorems have been cited. The latter are due to P. Gilkey, E. Puffini and V. Videv, and have been recently obtained. | | Source: | arXiv, math/0701090 | | Services: | Forum | Review | PDF | Favorites | |
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