Two classes of solutions for conformally at perfect uids exist depending on whether the uid expansion vanishes or not. The expanding solutions have become known as the Stephani universes and are generalisations of the well-known Friedmann-Robertson-Walker solutions; the solutions with zero expansion generalise the interior Schwarzschild solution. The isometry structure of the expansion-free sol...

We investigate the Hasse principles for isotropy and isometry of quadratic forms over finitely generated field extensions with respect to various sets discrete valuations. Over purely transcendental fields that satisfy property $\mathscr{A}_i(2)$ some $i$, we find numerous counterexamples principle a relatively small set For $K$ transcendence degree $r$ an algebraically closed characteristic $\...

This book presents the construction of finitely “twisted” Laplace operators whose spectrum determines covering equivalence two Riemannian manifolds.