اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA Classification Of Cohomogeneity One Actions On The Minkowski Space $mathbb{R}^{3,1}$
147
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The aim of this paper is to classify cohomogeneity one isometric actions on the 4-dimensional Minkowski space $mathbb{R}^{3,1}$, up to orbit equivalence. Representations, up to conjugacy, of the acting groups in $O(3,1)ltimes mathbb{R}^{3,1}$ are given in both cases, proper and non-proper actions. When the action is proper, the orbits and the orbit spaces are determined.
قيم البحث
اقرأ أيضاً
We construct examples of cohomogeneity one special Lagrangian submanifolds in the cotangent bundle over the complex projective space, whose Calabi-Yau structure was given by Stenzel. For each example, we describe the condition of special Lagrangian a
s an ordinary differential equation. Our method is based on a moment map technique and the classification of cohomogeneity one actions on the complex projective space classified by Takagi.
In this paper, we consider the evolution of spacelike graphic hypersurfaces defined over a convex piece of hyperbolic plane $mathscr{H}^{n}(1)$, of center at origin and radius $1$, in the $(n+1)$-dimensional Lorentz-Minkowski space $mathbb{R}^{n+1}_{
1}$ along the inverse Gauss curvature flow (i.e., the evolving speed equals the $(-1/n)$-th power of the Gaussian curvature) with the vanishing Neumann boundary condition, and prove that this flow exists for all the time. Moreover, we can show that, after suitable rescaling, the evolving spacelike graphic hypersurfaces converge smoothly to a piece of the spacelike graph of a positive constant function defined over the piece of $mathscr{H}^{n}(1)$ as time tends to infinity.
We extend V. Arnolds theory of asymptotic linking for two volume preserving flows on a domain in ${mathbb R}^3$ and $S^3$ to volume preserving actions of ${mathbb R}^k$ and ${mathbb R}^ell$ on certain domains in ${mathbb R}^n$ and also to linking of
a volume preserving action of ${mathbb R}^k$ with a closed oriented singular $ell$-dimensional submanifold in ${mathbb R}^n$, where $n=k+ell+1$. We also extend the Biot-Savart formula to higher dimensions.
We prove the hypersymplectic flow of simple type on standard torus $mathbb{T}^4$ exists for all time and converges to the standard flat structure modulo diffeomorphisms. This result in particular gives the first example of a cohomogeneity-one $G_2$-L
aplacian flow on a compact $7$-manifold which exists for all time and converges to a torsion-free $G_2$ structure modulo diffeomorphisms.
In this paper, we study biharmonic hypersurfaces in a product of an Einstein space and a real line. We prove that a biharmonic hypersurface with constant mean curvature in such a product is either minimal or a vertical cylinder generalizing a result
of cite{OW} and cite{FOR}. We derived the biharmonic equation for hypersurfaces in $S^mtimes mathbb{R}$ and $H^mtimes mathbb{R}$ in terms of the angle function of the hypersurface, and use it to obtain some classifications of biharmonic hypersurfaces in such spaces. These include classifications of biharmonic hypersurfaces which are totally umbilical or semi-parallel for $mge 3$, and some classifications of biharmonic surfaces in $S^2times mathbb{R}$ and $H^2times mathbb{R}$ which are constant angle or belong to certain classes of rotation surfaces.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
