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K-contact A-manifolds

WŁodzimierz Jelonek (1998)

Colloquium Mathematicae

The aim of this paper is to give a characterization of regular K-contact A-manifolds.

Kikkawa loops and homogeneous loops

Michihiko Kikkawa (2004)

Commentationes Mathematicae Universitatis Carolinae

In H. Kiechle's publication ``Theory of K-loops'' [3], the name Kikkawa loops is given to symmetric loops introduced by the author in 1973. This concept started from an analogical imagination of sum of vectors in Euclidean space brought up on a sphere. In 1975, this concept was extended by him to the more general concept of homogeneous loops, and it led us to a non-associative generalization of the theory of Lie groups. In this article, the backstage of finding these concepts will be disclosed from...

Killing spinor-valued forms and the cone construction

Petr Somberg, Petr Zima (2016)

Archivum Mathematicum

On a pseudo-Riemannian manifold 𝕄 we introduce a system of partial differential Killing type equations for spinor-valued differential forms, and study their basic properties. We discuss the relationship between solutions of Killing equations on 𝕄 and parallel fields on the metric cone over 𝕄 for spinor-valued forms.

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.

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