The Dirac operator on generalized Taub-NUT spaces

We find sufficient conditions for the absence of harmonic $L^2$ spinors on spin manifolds constructed as cone bundles over a compact K\"ahler base. These conditions are fulfilled for certain perturbations of the Euclidean metric, and also for the generalized Taub-NUT metrics of Iwai-Katayama, thus proving a conjecture of Vi\csinescu and the second author.Comment: Final version, 16 page

K\"ahlerian Twistor Spinors

On a K\"ahler spin manifold K\"ahlerian twistor spinors are a natural analogue of twistor spinors on Riemannian spin manifolds. They are defined as sections in the kernel of a first order differential operator adapted to the K\"ahler structure, called K\"ahlerian twistor (Penrose) operator. We study K\"ahlerian twistor spinors and give a complete description of compact K\"ahler manifolds of constant scalar curvature admitting such spinors. As in the Riemannian case, the existence of K\"ahlerian twistor spinors is related to the lower bound of the spectrum of the Dirac operator.Comment: shorter version; to appear in Math.

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

Rockfill Dam Stability Problems in a Seismic Zone

In the close vicinity of the great shock, March 4, 1977, in Vrancea region, Romania, one of the biggest shocks felt recently in Europe, two rockfill dams 120 m and, respectively, 70 m high with clayey cores are being constructed. In the paper, some problems arised by the design of these dams from earthquake engineering point of view are presented

Invariant four-forms and symmetric pairs

We give criteria for real, complex and quaternionic representations to define s-representations, focusing on exceptional Lie algebras defined by spin representations. As applications, we obtain the classification of complex representations whose second exterior power is irreducible or has an irreducible summand of co-dimension one, and we give a conceptual computation-free argument for the construction of the exceptional Lie algebras of compact type.Comment: 16 pages [v2: references added, last section expanded

Spectral Bounds for Dirac Operators on Open Manifolds

We extend several classical eigenvalue estimates for Dirac operators on compact manifolds to noncompact, even incomplete manifolds. This includes Friedrich's estimate for manifolds with positive scalar curvature as well as the author's estimate on surfaces.Comment: pdflatex, 14 pages, 3 figure

Pseudo-Riemannian manifolds with recurrent spinor fields

The existence of a recurrent spinor field on a pseudo-Riemannian spin manifold $(M,g)$ is closely related to the existence of a parallel 1-dimensional complex subbundle of the spinor bundle of $(M,g)$. We characterize the following simply connected pseudo-Riemannian manifolds admitting such subbundles in terms of their holonomy algebras: Riemannian manifolds; Lorentzian manifolds; pseudo-Riemannian manifolds with irreducible holonomy algebras; pseudo-Riemannian manifolds of neutral signature admitting two complementary parallel isotropic distributions.Comment: 13 pages, the final versio

A characterization of Dirac morphisms

Relating the Dirac operators on the total space and on the base manifold of a horizontally conformal submersion, we characterize Dirac morphisms, i.e. maps which pull back (local) harmonic spinor fields onto (local) harmonic spinor fields.Comment: 18 pages; restricted to the even-dimensional cas