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Killing tensors and warped product

Włodzimierz Jelonek (2000)

Annales Polonici Mathematici

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 X ϱ ( X , X ) = 2 / ( n + 2 ) X τ g ( X , X )

Killing's equations in dimension two and systems of finite type

Gerard Thompson (1999)

Mathematica Bohemica

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.

Knit products of graded Lie algebras and groups

Michor, Peter W. (1990)

Proceedings of the Winter School "Geometry and Physics"

Let A = k A k and B = k B k be graded Lie algebras whose grading is in 𝒵 or 𝒵 2 , but only one of them. Suppose that ( α , β ) is a derivatively knitted pair of representations for ( A , B ) , i.e. α and β satisfy equations which look “derivatively knitted"; then A B : = k , l ( A k B l ) , endowed with a suitable bracket, which mimics semidirect products on both sides, becomes a graded Lie algebra A ( α , β ) B . This graded Lie algebra is called the knit product of A and B . The author investigates the general situation for any graded Lie subalgebras A and B of a graded...

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