In this paper, we study the existence, uniqueness and asymptotic behavior of rotationally symmetric translating solitons of the mean curvature flow in Minkowski space. We also study the asymptotic behavior and the strict convexity of general solitons of such flows.

Using Margulis’s results on lattices in semisimple Lie groups, we prove the GrothendieckKatz p-Curvature Conjecture for certain locally symmetric varieties, including the moduli space of abelian varieties Ag when g > 1.

By using new algebraic techniques, two Casorati inequalities are established for submanifolds in a Riemannian manifold of quasi-constant curvature with a semi-symmetric metric connection, which generalize inequalities obtained by Lee et al. J. Inequal. Appl. 2014, 2014, 327.

M . Ratner's theorem on the rigidity of horocycle flows is extended to the rigidity of horospherical foliations on bundles over finite-volume locally-symmetric spaces of non-positive sectional curvature, and to other foliations of the same algebraic form.

We derive matter collineations for some static spherically symmetric spacetimes and compare the results with Killing, Ricci and Curvature symmetries. We conclude that matter and Ricci collineations are not, in general, the same.

We study the isometry groups of a family of complete p + 2curvature homogeneous pseudo-Riemannian metrics on R which have neutral signature (3 + 2p, 3 + 2p), and which are 0-curvature modeled on an indecomposible symmetric space.

Using Margulis’s results on lattices in semisimple Lie groups, we prove the GrothendieckKatz p-Curvature Conjecture for many locally symmetric varieties, including HilbertBlumenthal modular varieties and the moduli space of abelian varieties Ag when g > 1.

In [18], using polylinear mappings, we obtained several curvature tensors in the space LN with non-symmetric affine connection ∇. By the same method, we here examine Ricci type identities.

The classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit “hidden symmetry” from conformal KillingYano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike codimension-two submanifolds in a static spherically symmetric spacetime: a codimensiontwo submanifold with constant normalized null expansion (null mean curva...

The classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit “hidden symmetry” from conformal KillingYano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike codimension-two submanifolds in a static spherically symmetric spacetime: a codimensiontwo submanifold with constant normalized null expansion (null mean curva...