arXiv subjects
Publications and source records attributed to Zhivko Zhelev.
In the article we prove some inequalities that contain relations between altitudes and medians in triangle. At least one of these inequalities has not been considered in the literature before and the main theorem has also not been proved elsewhere in that form. Some immediate corollaries have been presented as well.
We consider four-dimensional Riemannian manifolds with commuting higher order Jacobi operators defined on two-dimensional orthogonal subspaces (polygons) and on their orthogonal subspaces. 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. $\mathcal{J}(X)\circ\mathcal{J}(X^{\perp})=\mathcal{J}(X^{\perp})\circ \mathcal{J}(X)$. 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.