arXiv subjects
Publications and source records attributed to Assen Bojilov.
We show that a $3-$dimensional paracontact manifold on which $Qφ=φQ$ is either a manifold with $trh^2=0$, flat or of constant $ξ-$sectional curvature $k\neq-1$ and constant $φ$-sectional curvature $-k\neq 1$.
In this paper, we address the problem for enumerating the number of finite field elements with prescribed trace and co-trace in case of arbitrary characteristic $p$. We show that this problem can be reduced to solving a system of $p-1$ linear equations with matrix of coefficients a slight modification of circulant matrix formed by the Kloosterman sums over the field $\MF_{p}$. The presented approach is illustrated in the cases of characteristic $p = 2,3$ and $5$.