Courant morphisms and moment maps

Coalgebra Morphisms Subsume Open Maps

The Geometry of Harmonic Maps and Morphisms

We give a survey of harmonic morphisms between Riemannian manifolds, concentrating on their construction and relations with the geometry of foliations.

Infinitesimal Deformations of Harmonic Maps and Morphisms

Harmonic maps are mappings between Riemannian manifolds which extremize a natural energy functional. They have been studied for many years in differential geometry, and in particle physics as nonlinear sigma models. We shall report on recent progress in understanding their infinitesimal deformations, the so-called Jacobi fields. It is important to know whether the Jacobi fields along harmonic m...

D/G-valued moment maps

We study Dirac structures associated with Manin pairs (d, g) and give a Dirac geometric approach to Hamiltonian spaces with D/G-valued moment maps, originally introduced by Alekseev and Kosmann-Schwarzbach [3] in terms of quasi-Poisson structures. We explain how these two distinct frameworks are related to each other, proving that they lead to isomorphic categories of Hamiltonian spaces. We str...

Complete Lifts of Harmonic Maps and Morphisms between Euclidean Spaces

We introduce the complete lifts of maps between (real and complex) Euclidean spaces and study their properties concerning holomorphicity, harmonicity and horizontal weakly conformality. As applications, we are able to use this concept to characterize holomorphic maps φ : C ⊃ U −→ C (Proposition 2.3) and to construct many new examples of harmonic morphisms (Theorem 3.3). Finally we show that the...