Geometries arising from trilinear forms on low-dimensional vector spaces

Orbit Spaces Arising from Isometric Actions on Hyperbolic Spaces

Let be a differentiable action of a Lie group on a differentiable manifold and consider the orbit space with the quotient topology.  Dimension of is called the cohomogeneity of the action of  on . If is a differentiable manifold  of  cohomogeneity one under the action of  a compact and connected Lie group, then the orbit space is homeomorphic to one of the spaces , , or . In this paper we suppo...

On Canonical Binary Trilinear Forms

Quaternary binary trilinear forms

Dear friends, In 1997 or 1998 I began to write a paper [20], trying to extend the known description of binary forms of norm unity, in the real or complex cases, to the case of quaternions, but I never finished it. In 2002, I resumed my work but then I was unable to understand what I had done, so I made a fresh start with somewhat different assumptions. Now I have realized that this was a gross ...

On the Structure of Bounded Trilinear Forms

0. Introduction. In previous work CKP1], CKP2] the authors have initiated a study of Schatten-von Neumann classes of trilinear forms in Hilbert space. We believe however that, in order to progress further, it is necessary to gain a better understanding of the structure of bounded forms, and of compact ones. This is a rather intricate problem. Accordingly, in this paper we have collected various...

Conformally invariant trilinear forms on the sphere

To each complex number λ is associated a representation πλ of the conformal group SO0(1, n) on C∞(Sn−1) (spherical principal series). For three values λ1, λ2, λ3, we construct a trilinear form on C∞(Sn−1)×C∞(Sn−1)×C∞(Sn−1), which is invariant by πλ1 ⊗πλ2 ⊗ πλ3 . The trilinear form, first defined for (λ1, λ2, λ3) in an open set of C is extended meromorphically, with simple poles located in an ex...