Killing tensors and warped product
We present some examples of Killing tensors and give their geometric interpretation. We give new examples of non-compact complete and compact Riemannian manifolds whose Ricci tensor ϱ satisfies the condition
We present some examples of Killing tensors and give their geometric interpretation. We give new examples of non-compact complete and compact Riemannian manifolds whose Ricci tensor ϱ satisfies the condition
A PDE system is said to be of finite type if all possible derivatives at some order can be solved for in terms lower order derivatives. An algorithm for determining whether a system of finite type has solutions is outlined. The results are then applied to the problem of characterizing symmetric linear connections in two dimensions that possess homogeneous linear and quadratic integrals of motions, that is, solving Killing's equations of degree one and two.
Let and be graded Lie algebras whose grading is in or , but only one of them. Suppose that is a derivatively knitted pair of representations for , i.e. and satisfy equations which look “derivatively knitted"; then , endowed with a suitable bracket, which mimics semidirect products on both sides, becomes a graded Lie algebra . This graded Lie algebra is called the knit product of and . The author investigates the general situation for any graded Lie subalgebras and of a graded...