Transformations of locally conformally K\"ahler manifolds

We consider several transformation groups of a locally conformally K\"ahler manifold and discuss their inter-relations. Among other results, we prove that all conformal vector fields on a compact Vaisman manifold which is neither locally conformally hyperk\"ahler nor a diagonal Hopf manifold are Killing, holomorphic and that all affine vector fields with respect to the minimal Weyl connection of a locally conformally K\"ahler manifold which is neither Weyl-reducible nor locally conformally hyperk\"ahler are holomorphic and conformalComment: 8 page

Tight Beltrami fields with symmetry

Let $M$ be a compact orientable Seifered fibered 3-manifold without a boundary, and $\alpha$ an $S^1$-invariant contact form on $M$. In a suitable adapted Riemannian metric to $\alpha$, we provide a bound for the volume $\text{Vol}(M)$ and the curvature, which implies the universal tightness of the contact structure $\xi=\ker\alpha$.Comment: 26 page

Hidden symmetries and Killing tensors on curved spaces

Higher order symmetries corresponding to Killing tensors are investigated. The intimate relation between Killing-Yano tensors and non-standard supersymmetries is pointed out. In the Dirac theory on curved spaces, Killing-Yano tensors generate Dirac type operators involved in interesting algebraic structures as dynamical algebras or even infinite dimensional algebras or superalgebras. The general results are applied to space-times which appear in modern studies. One presents the infinite dimensional superalgebra of Dirac type operators on the 4-dimensional Euclidean Taub-NUT space that can be seen as a twisted loop algebra. The existence of the conformal Killing-Yano tensors is investigated for some spaces with mixed Sasakian structures.Comment: 12 pages; talk presented at Group 27 Colloquium, Yerevan, Armenia, August 200

On the Weyl tensor of a self-dual complex 4-manifold

Consiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7 Rome / CNR - Consiglio Nazionale delle RichercheSIGLEITItal