ترغب بنشر مسار تعليمي؟ اضغط هنا

New Minimal Hypersurfaces in R(k+1)(2k+1) and S(2k+3)k

137   0   0.0 ( 0 )
 نشر من قبل Georgios Linardopoulos
 تاريخ النشر 2016
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We find a class of minimal hypersurfaces H(k) as the zero level set of Pfaffians, resp. determinants of real 2k+2 dimensional antisymmetric matrices. While H(1) and H(2) are congruent to a 6-dimensional quadratic cone resp. Hsiangs cubic su(4) invariant in R15, H(k>2) (special harmonic so(2k+2)-invariant cones of degree>3) seem to be new.

قيم البحث

اقرأ أيضاً

169 - Ruoxu Cen , Ran Duan , Yong Gu 2019
A roundtrip spanner of a directed graph $G$ is a subgraph of $G$ preserving roundtrip distances approximately for all pairs of vertices. Despite extensive research, there is still a small stretch gap between roundtrip spanners in directed graphs and undirected graphs. For a directed graph with real edge weights in $[1,W]$, we first propose a new deterministic algorithm that constructs a roundtrip spanner with $(2k-1)$ stretch and $O(k n^{1+1/k}log (nW))$ edges for every integer $k> 1$, then remove the dependence of size on $W$ to give a roundtrip spanner with $(2k-1)$ stretch and $O(k n^{1+1/k}log n)$ edges. While keeping the edge size small, our result improves the previous $2k+epsilon$ stretch roundtrip spanners in directed graphs [Roditty, Thorup, Zwick02; Zhu, Lam18], and almost matches the undirected $(2k-1)$-spanner with $O(n^{1+1/k})$ edges [Althofer et al. 93] when $k$ is a constant, which is optimal under Erdos conjecture.
A diagonal metric sum_{i=1}^n g_{ii} dx_i^2 is termed Guichard_k if sum_{i=1}^{n-k}g_{ii}-sum_{i=n-k+1}^n g_{ii}=0. A hypersurface in R^{n+1} is isothermic_k if it admits line of curvature co-ordinates such that its induced metric is Guichard_k. Isot hermic_1 surfaces in R^3 are the classical isothermic surfaces in R^3. Both isothermic_k hypersurfaces in R^{n+1} and Guichard_k orthogonal co-ordinate systems on R^n are invariant under conformal transformations. A sequence of n isothermic_k hypersurfaces in R^{n+1} (Guichard_k orthogonal co-ordinate systems on R^n resp.) is called a Combescure sequence if the consecutive hypersurfaces (orthogonal co-ordinate systems resp.) are related by Combescure transformations. We give a correspondence between Combescure sequences of Guichard_k orthogonal co-ordinate systems on R^n and solutions of the O(2n-k,k)/O(n)xO(n-k,k)-system, and a correspondence between Combescure sequences of isothermic_k hypersurfaces in R^{n+1} and solutions of the O(2n+1-k,k)/O(n+1)xO(n-k,k)-system, both being integrable systems. Methods from soliton theory can therefore be used to construct Christoffel, Ribaucour, and Lie transforms, and to describe the moduli spaces of these geometric objects and their loop group symmetries.
151 - R. S. Ward 2016
This letter describes a completely-integrable system of Yang-Mills-Higgs equations which generalizes the Hitchin equations on a Riemann surface to arbitrary k-dimensional complex manifolds. The system arises as a dimensional reduction of a set of int egrable Yang-Mills equations in 4k real dimensions. Our integrable system implies other generalizations such as the Simpson equations and the non-abelian Seiberg-Witten equations. Some simple solutions in the k=2 case are described.
70 - P. Grinza , B. Ponsot 2004
Massless flows between the coset model su(2)_{k+1} otimes su(2)_k /su(2)_{2k+1} and the minimal model M_{k+2} are studied from the viewpoint of form factors. These flows include in particular the flow between the Tricritical Ising model and the Ising model. Form factors of the trace operator with an arbitrary number of particles are constructed, and numerical checks on the central charge are performed with four particles contribution. Large discrepancies with respect to the exact results are observed in most cases.
Given a hypersurface $M$ of null scalar curvature in the unit sphere $mathbb{S}^n$, $nge 4$, such that its second fundamental form has rank greater than 2, we construct a singular scalar-flat hypersurface in $Rr^{n+1}$ as a normal graph over a trunca ted cone generated by $M$. Furthermore, this graph is 1-stable if the cone is strictly 1-stable.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا