Harmonicity of $(\varphi,\varphi^{\prime})$-holomorphic sections of a (semi-riemannian) almost paracontact fiber bundle of type II

In this paper (ϕ, ϕ0 )-holomorphic maps from an almost paraHermitian manifold to an almost paracontact metric manifold are studied and a criterion for the harmonicity of such (ϕ, ϕ0 )-holomorphic maps is obtained. Also (ϕ, ϕ0 )-holomorphic sections of (semi−Riemannian) almost paracontact fiber bundles of type II are studied and a criterion for the harmonicity of such (ϕ, ϕ0 )-holomorphic sections is obtained.

Harmonicity of $(\varphi,\varphi^{\prime})$-holomorphic sections of a (semi-riemannian) almost paracontact fiber bundle of type II

In this paper (ϕ, ϕ0 )-holomorphic maps from an almost paraHermitian manifold to an almost paracontact metric manifold are studied and a criterion for the harmonicity of such (ϕ, ϕ0 )-holomorphic maps is obtained. Also (ϕ, ϕ0 )-holomorphic sections of (semi−Riemannian) almost paracontact fiber bundles of type II are studied and a criterion for the harmonicity of such (ϕ, ϕ0 )-holomorphic sections is obtained.

Extension of cohomology classes and holomorphic sections defined on subvarieties

In this paper, we obtain two extension theorems for cohomology classes and holomorphic sections defined on analytic subvarieties, which are defined as the supports of the quotient sheaves of multiplier ideal sheaves of quasi-plurisubharmonic functions with arbitrary singularities. The first result gives a positive answer to a question posed by Cao-Demailly-Matsumura and unifies a few well-known injectivity theorems. The second result generalizes and optimizes a general L 2 L^2 extension theorem obtained by Demailly.

Energy of sections of the Deligne–Hitchin twistor space

We study a natural functional on the space of holomorphic sections of the Deligne–Hitchin moduli space of a compact Riemann surface, generalizing the energy of equivariant harmonic maps corresponding to twistor lines. We show that the energy is the residue of the pull-back along the section of a natural meromorphic connection on the hyperholomorphic line bundle recently constructed by Hitchin. As a byproduct, we show the existence of a hyper-Kähler potentials for new components of real holomorphic sections of twistor spaces of hyper-Kähler manifolds with rotating $$S^1$$ S 1 -action. Additionally, we prove that for a certain class of real holomorphic sections of the Deligne–Hitchin moduli space, the energy functional is basically given by the Willmore energy of corresponding equivariant conformal map to the 3-sphere. As an application we use the functional to distinguish new components of real holomorphic sections of the Deligne–Hitchin moduli space from the space of twistor lines.

The index of harmonic maps from surfaces to complex projective spaces

We estimate the dimensions of the spaces of holomorphic sections of certain line bundles to give improved lower bounds on the index of complex isotropic harmonic maps to complex projective space from the sphere and torus, and in some cases from higher genus surfaces.

Rigidity properties of holomorphic Legendrian singularities

We study the singularities of Legendrian subvarieties of contact manifolds in the complex-analytic category and prove two rigidity results. The first one is that Legendrian singularities with reduced tangent cones are contactomorphically biholomorphic to their tangent cones. This result is partly motivated by a problem on Fano contact manifolds. The second result is the deformation-rigidity of normal Legendrian singularities, meaning that any holomorphic family of normal Legendrian singularities is trivial, up to contactomorphic biholomorphisms of germs. Both results are proved by exploiting the relation between infinitesimal contactomorphisms and holomorphic sections of the natural line bundle on the contact manifold. Comment: 21 pages, minor revision