Allan Freitas, Henrique F. de Lima, Márcio S. Santos, Joyce S. Sindeaux
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引用次数: 0
摘要
我们研究了一类重要的捕获子流形特例的不存在性和刚度,与闭共形类时向量场(\mathcal K=f(t)\partial _t)(\(t\ in I\subet \mathbb R\))相关的n维类空平均曲率流孤子,该向量场全局定义在具有翘曲函数(f\ in C^\infty(I)\)和黎曼纤维(M^{n+p}\)的(((n+p+1)\)维广义Robertson–Walker(GRW)时空上,通过适当的广义极大值原理的应用,并在f和\(M^{n+p}\)的曲率的某些约束下。在余维1中,我们还获得了关于GRW时空中类空平均曲率流孤子方程的新的Calabi–Bernstein型结果。
Nonexistence and rigidity of spacelike mean curvature flow solitons immersed in a GRW spacetime
We study the nonexistence and rigidity of an important class of particular cases of trapped submanifolds, more precisely, n-dimensional spacelike mean curvature flow solitons related to the closed conformal timelike vector field \(\mathcal K=f(t)\partial _t\) (\(t\in I\subset \mathbb R\)) which is globally defined on an \((n+p+1)\)-dimensional generalized Robertson–Walker (GRW) spacetime \(-I\times _fM^{n+p}\) with warping function \(f\in C^\infty (I)\) and Riemannian fiber \(M^{n+p}\), via applications of suitable generalized maximum principles and under certain constraints on f and on the curvatures of \(M^{n+p}\). In codimension 1, we also obtain new Calabi–Bernstein-type results concerning the spacelike mean curvature flow soliton equation in a GRW spacetime.
期刊介绍:
This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field.
The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.