ﻻ يوجد ملخص باللغة العربية
Let $M^n$ be a closed Riemannian manifold on which the integral of the scalar curvature is nonnegative. Suppose $mathfrak{a}$ is a symmetric $(0,2)$ tensor field whose dual $(1,1)$ tensor $mathcal{A}$ has $n$ distinct eigenvalues, and $mathrm{tr}(mathcal{A}^k)$ are constants for $k=1,cdots, n-1$. We show that all the eigenvalues of $mathcal{A}$ are constants, generalizing a theorem of de Almeida and Brito cite{dB90} to higher dimensions. As a consequence, a closed hypersurface $M^n$ in $S^{n+1}$ is isoparametric if one takes $mathfrak{a}$ above to be the second fundamental form, giving affirmative evidence to Cherns conjecture.
We generalize the concept of the group determinant and prove a necessary and sufficient novel condition for a subset to be a subgroup. This development is based on the group determinant work by Edward Formanek, David Sibley, and Richard Mansfield, wh
Several counterexample models to the Nelson-Seiberg theorem have been discovered in previous literature, with generic superpotentials respecting the R-symmetry and non-generic R-charge assignments for chiral fields. This work present a sufficient con
Mean curvature flow for isoparametric submanifolds in Euclidean spaces and spheres was studied by the authors in [LT]. In this paper, we will show that all these solutions are ancient solutions. We also discuss rigidity of ancient mean curvature flow
Let $D$ be a disk in $mathbb{R}^n$ and $fin C^{r+2}(D, mathbb{R}^k)$. We deal with the problem of the algebraic approximation of the set $j^{r}f^{-1}(W)$ consisting of the set of points in the disk $D$ where the $r$-th jet extension of $f$ meets a gi
Based on the general form of entanglement witnesses constructed from separable states, we first show a sufficient condition of violating the structural physical approximation (SPA) conjecture [Phys. Rev. A 78, 062105 (2008)]. Then we discuss the SPA