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# Isoparametric surfaces in $\mathbb{E}(\kappa,\tau)$-spaces

We provide an explicit classification of the following four families of surfaces in any homogeneous 3-manifold with 4-dimensional isometry group:

• isoparametric surfaces,
• surfaces with constant principal curvatures,
• extrinsically homogeneous surfaces,
• $H$-surfaces with vanishing Abresch-Rosenberg differential.
This is a joint work with Miguel Domínguez Vázquez.

Seminario 1ª planta, IEMath-GR

# Some results of invariant theory for CR-manifolds

## Yen-Chang Huang Xinyang Normal University

In this talk, I will introduce some recent works of invariant theory on CR manifolds. After a briefing of CR manifolds, some integral invariants will be introduced in the Heisenberg groups (regarded as a flat model of CR manifolds). The invariants are not changed in the sense of the pseudo-hermitian transformations which can be regarded as the rigid motions in the Heisenberg groups. We take the approach from Integral Geometry for convex bodies, but in our case, the assumption of convexity is not necessary. The applications can be implemented to the CR-version of the Crofton's formula and the containment problems with other related. Some recent development in the invariant theory for CR manifolds will also be discussed in the end of the talk.

Seminario 1ª planta, IEMath-GR

# Esko Heinonen

Despacho: D2 IEMath

# Franc Forstneric

## Univerza v Ljubljani

Despacho: Planta Baja, nº 5

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