ترغب بنشر مسار تعليمي؟ اضغط هنا

Injectivity radius and optimal regularity of Lorentzian manifolds with bounded curvature

176   0   0.0 ( 0 )
 نشر من قبل Philippe G. LeFloch
 تاريخ النشر 2008
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

We review recent work on the local geometry and optimal regularity of Lorentzian manifolds with bounded curvature. Our main results provide an estimate of the injectivity radius of an observer, and a local canonical foliations by CMC (Constant Mean Curvature) hypersurfaces, together with spatially harmonic coordinates. In contrast with earlier results based on a global bound for derivatives of the curvature, our method requires only a sup-norm bound on the curvature near the given observer.



قيم البحث

اقرأ أيضاً

110 - Philippe G. LeFloch 2008
We consider pointed Lorentzian manifolds and construct canonical foliations by constant mean curvature (CMC) hypersurfaces. Our result assumes a uniform bound on the local sup-norm of the curvature of the manifold and on its local injectivity radius, only. The prescribed curvature problem under consideration is a nonlinear elliptic equation whose coefficients have limited regularity. The CMC foliation allows us to introduce CMC-harmonic coordinates, in which the coefficients of the Lorentzian metric have optimal regularity.
294 - R. Milson , N. Pelavas 2007
We prove that a four-dimensional Lorentzian manifold that is curvature homogeneous of order 3, or $CH_3$ for short, is necessarily locally homogeneous. We also exhibit and classify four-dimensional Lorentzian, $CH_2$ manifolds that are not homogeneous.
81 - Quang-Tu Bui 2020
Using Lie groupoids, we prove that the injectivity radius of a manifold with a Lie structure at infinity is positive.
A mixed type surface is a connected regular surface in a Lorentzian 3-manifold with non-empty spacelike and timelike point sets. The induced metric of a mixed type surface is a signature-changing metric, and their lightlike points may be regarded as singular points of such metrics. In this paper, we investigate the behavior of Gaussian curvature at a non-degenerate lightlike point of a mixed type surface. To characterize the boundedness of Gaussian curvature at a non-degenerate lightlike points, we introduce several fundamental invariants along non-degenerate lightlike points, such as the lightlike singular curvature and the lightlike normal curvature. Moreover, using the results by Pelletier and Steller, we obtain the Gauss-Bonnet type formula for mixed type surfaces with bounded Gaussian curvature.
161 - E. Garcia-Rio , P. Gilkey , 2012
k-Curvature homogeneous three-dimensional Walker metrics are described for k=0,1,2. This allows a complete description of locally homogeneous three-dimensional Walker metrics, showing that there exist exactly three isometry classes of such manifolds. As an application one obtains a complete description of all locally homogeneous Lorentzian manifolds with recurrent curvature. Moreover, potential functions are constructed in all the locally homogeneous manifolds resulting in steady gradient Ricci and Cotton solitons.
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