اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدClassification of codimension two deformations of rank two Riemannian manifolds
149
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The purpose of this work is to close the local deformation problem of rank two Euclidean submanifolds in codimension two by describing their moduli space of deformations. In the process, we provide an explicit simple representation of these submanifolds, a result of independent interest by its applications. We also determine which deformations are genuine and honest, allowing us to find the first known examples of honestly locally deformable rank two submanifolds in codimension two. In addition, we study which of these submanifolds admit isometric immersions as Euclidean hypersurfaces, a property that gives rise to several applications to the Sbrana-Cartan theory of deformable Euclidean hypersurfaces.
قيم البحث
اقرأ أيضاً
In this paper we classify Euclidean hypersurfaces $fcolon M^n rightarrow mathbb{R}^{n+1}$ with a principal curvature of multiplicity $n-2$ that admit a genuine conformal deformation $tilde{f}colon M^n rightarrow mathbb{R}^{n+2}$. That $tilde{f}colon
M^n rightarrow mathbb{R}^{n+2}$ is a genuine conformal deformation of $f$ means that it is a conformal immersion for which there exists no open subset $U subset M^n$ such that the restriction $tilde{f}|_U$ is a composition $tilde f|_U=hcirc f|_U$ of $f|_U$ with a conformal immersion $hcolon Vto mathbb{R}^{n+2}$ of an open subset $Vsubset mathbb{R}^{n+1}$ containing $f(U)$.
We define Seiberg-Witten equations on closed manifolds endowed with a Riemannian foliation of codimension 4. When the foliation is taut, we show compactness of the moduli space under some hypothesis satisfied for instance by closed K-contact manifold
s. Furthermore, we prove some vanishing and non-vanishing results and we highlight that the invariants may be used to distinguish different foliations on diffeomorphic manifolds.
We describe all affine maps from a Riemannian manifold to a metric space and all possible image spaces.
A {em 2-Riemannian manifold} is a differentiable manifold exhibiting a 2-inner product on each tangent space. We first study lower dimensional 2-Riemannian manifolds by giving necessary and sufficient conditions for flatness. Afterward we associate t
o each 2-Riemannian manifold a unique torsion free compatible pseudoconnection. Using it we define a curvature for 2-Riemannian manifolds and study its properties. We also prove that 2-Riemannian pseudoconnections do not have Koszul derivatives. Moreover, we define stationary vector field with respect to a 2-Riemannian metric and prove that the stationary vector fields in $mathbb{R}^2$ with respect to the 2-Riemannian metric induced by the Euclidean product are the divergence free ones.
We provide a parametric construction in terms of minimal surfaces of the Euclidean submanifolds of codimension two and arbitrary dimension that attain equality in an inequality due to De Smet, Dillen, Verstraelen and Vrancken. The latter involves the
scalar curvature, the norm of the normal curvature tensor and the length of the mean curvature vector.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
