Deformations of harmonic mappings and variation of the energy
| Autor: | Spinaci, Marco |
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| Rok vydání: | 2013 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study the deformations of twisted harmonic maps $f$ with respect to the representation $\rho$. After constructing a continuous "universal" twisted harmonic map, we give a construction of every first order deformation of $f$ in terms of Hodge theory; we apply this result to the moduli space of reductive representations of a K\"ahler group, to show that the critical points of the energy functional $E$ coincide with the monodromy representations of polarized complex variations of Hodge structure. We then proceed to second order deformations, where obstructions arise; we investigate the existence of such deformations, and give a method for constructing them, as well. Applying this to the energy functional as above, we prove (for every finitely presented group) that the energy functional is a potential for the K\"ahler form of the "Betti" moduli space; assuming furthermore that the group is K\"ahler, we study the eigenvalues of the Hessian of $E$ at critical points. Comment: 32 pages. Several typos have been corrected and some references have been added. To appear on Math. Z |
| Databáze: | arXiv |
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