اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدRicci solitons and concurrent vector fields
110
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
A Ricci soliton $(M^n,g,v,lambda)$ on a Riemannian manifold $(M^n,g)$ is said to have concurrent potential field if its potential field $v$ is a concurrent vector field. In the first part of this paper we completely classify Ricci solitons with concurrent potential fields. In the second part we derive a necessary and sufficient condition for a submanifold to be a Ricci soliton in a Riemannian manifold equipped with a concurrent vector field. In the last part, we classify shrinking Ricci solitons with $lambda=1$ on Euclidean hypersurfaces. Several applications of our results are also presented.
قيم البحث
اقرأ أيضاً
The homogeneous affine surfaces have been classified by Opozda. They may be grouped into 3 families, which are not disjoint. The connections which arise as the Levi-Civita connection of a surface with a metric of constant Gauss curvature form one fam
ily; there are, however, two other families. For a surface in one of these other two families, we examine the Lie algebra of affine Killing vector fields and we give a complete classification of the homogeneous affine gradient Ricci solitons. The rank of the Ricci tensor plays a central role in our analysis.
In this paper we introduce, in the Riemannian setting, the notion of conformal Ricci soliton, which includes as particular cases Einstein manifolds, conformal Einstein manifolds and (generic and gradient) Ricci solitons. We provide here some necessar
y integrability conditions for the existence of these structures that also recover, in the corresponding contexts, those already known in the literature for conformally Einstein manifolds and for gradient Ricci solitons. A crucial tool in our analysis is the construction of some appropriate and highly nontrivial $(0,3)$-tensors related to the geometric structures, that in the special case of gradient Ricci solitons become the celebrated tensor $D$ recently introduced by Cao and Chen. A significant part of our investigation, which has independent interest, is the derivation of a number of commutation rules for covariant derivatives (of functions and tensors) and of transformation laws of some geometric objects under a conformal change of the underlying metric.
We describe three-dimensional Lorentzian homogeneous Ricci solitons, showing that all types (i.e. shrinking, expanding and steady) exist. Moreover, all non-trivial examples have non-diagonalizable Ricci operator with one only eigenvalue.
In $N(k)$-contact metric manifolds and/or $(k,mu)$-manifolds, gradient Ricci solitons, compact Ricci solitons and Ricci solitons with $V$ pointwise collinear with the structure vector field $xi $ are studied.
The aim of this paper is to prove some classification results for generic shrinking Ricci solitons. In particular, we show that every three dimensional generic shrinking Ricci soliton is given by quotients of either $mathds{S}^3$, $erretimesmathds{S}
^2$ or $erre^3$, under some very weak conditions on the vector field $X$ generating the soliton structure. In doing so we introduce analytical tools that could be useful in other settings; for instance we prove that the Omori-Yau maximum principle holds for the $X$-Laplacian on every generic Ricci soliton, without any assumption on $X$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
