Isotropic almost complex structures and harmonic unit vector fields

Harmonic-killing Vector Fields *

In this paper we consider the harmonicity of the 1-parameter group of local infinitesimal transformations associated to a vector field on a (pseudo-) Riemannian manifold to study this class of vector fields, which we call harmonic-Killing vector fields.

8-th International Workshop on Complex structures and vector fields

Embedded Surfaces and Almost Complex Structures

In this paper, we prove necessary and sufficient conditions for a smooth surface in a smooth 4-manifold X to be pseudoholomorphic with respect to an almost complex structure on X. In particular, this provides a systematic approach to the construction of pseudoholomorphic curves that do not minimize the genus in their homology class.

Almost Complex Projective Structures and Their Morphisms

We discuss almost complex projective geometry and the relations to a distinguished class of curves. We present the geometry from the viewpoint of the theory of parabolic geometries and we shall specify the classical generalizations of the concept of the planarity of curves to this case. In particular, we show that the natural class of J-planar curves coincides with the class of all geodesics of...

Symplectomorphism Groups and Almost Complex Structures

This paper studies groups of symplectomorphisms of ruled surfaces M for symplectic forms with varying cohomology class. This cohomology class is characterised by the ratio μ of the size of the base to that of the fiber. By considering appropriate spaces of almost complex structures, we investigate how the topological type of these groups changes as μ increases. If the base is a sphere, this cha...