Propagation of symmetries for Ricci shrinkers

Smooth Compactness of Self-shrinkers

We prove a smooth compactness theorem for the space of embedded selfshrinkers in R. Since self-shrinkers model singularities in mean curvature flow, this theorem can be thought of as a compactness result for the space of all singularities and it plays an important role in studying generic mean curvature flow. 0. Introduction A surface Σ ⊂ R is said to be a self-shrinker if it satisfies (0.1) H ...

Conservation Laws and Associated Lie Symmetries for the 2d Ricci Flow Model∗

The paper presents a connection between Lie symmetries and conservation laws for the 2D Ricci flow model.The procedure starts by obtaining a set of multipliers which generates conservation laws.Then, taking into account the most general form of multiplier and making use of a relation which connects Lie symmetries and conservation laws for any dynamical system, one determines associated symmetry...

Ricci tensor for $GCR$-lightlike submanifolds of indefinite Kaehler manifolds

We obtain the expression of Ricci tensor for a $GCR$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $GCR$-lightlike submanifold of anindefinite complex space form. Moreover, we have proved that everyproper totally umbilical $GCR$-lightlike submanifold of anindefinite Kaehler manifold is a totally geodesic $GCR$-lightlikesubmanifold.

Ricci Lower Bound for Kähler–ricci Flow

Symmetries of the Ricci Tensor of Static Space-times with Maximal Symmetric Transverse Spaces

Static space times with maximal symmetric transverse spaces are classified according to their Ricci collineations. These are investigated for non-degenerate Ricci tensor (det.(Rα) 6= 0). It turns out that the only collineations admitted by these spaces can be ten, seven, six or four. Some new metrics admitting proper Ricci collineations are also investigated. PACS numbers: 04.20.-q, 04.20.Jb