Stability of Harmonic Morphisms to a Surface
نویسنده
چکیده
Using the fact that harmonic morphisms to a surface have minimal bres, links between the volume-stability of the bres and the energy-stability of the map are found for manifolds without boundary. A stability result for harmonic morphisms from a manifold with boundary to a Riemann surface is also established.
منابع مشابه
Stability of Harmonic Morphisms
We study the stability of harmonic morphisms as a subclass of harmonic maps. As a general result we show that any harmonic morphism to a manifold of dimension at least three is stable with respect to some Riemannian metric on the target. Furthermore we link the index and nullity of the composition of harmonic morphisms with the index and nullity of the composed maps.
متن کاملHarmonic Morphisms from Three-dimensional Euclidean and Spherical Space Forms
This paper gives a description of all harmonic morphisms from a threedimensional non-simply-connected Euclidean and spherical space form to a surface, by extending the work of Baird-Wood [4, 5] who dealt with the simply-connected case; namely we show that any such harmonic morphism is the composition of a “standard” harmonic morphism and a weakly conformal map. To complete the description we li...
متن کاملHarmonic Morphisms from Minkowski Space and Hyperbolic Numbers
We show that all harmonic morphisms from 3-dimensional Minkowski space with values in a surface have a Weierstrass representation involving the complex numbers or the hyperbolic numbers depending on the signature of the codomain. We deduce that there is a nontrivial globally defined submersive harmonic morphism from Minkowski 3-space to a surface, in contrast to the Riemannian case. We show tha...
متن کاملHarmonic Morphisms, Hermitian Structures and Symmetric Spaces
[A] M. Svensson, On holomorphic harmonic morphisms, Manuscripta Math. 107 (2002), 1–13. [B] M. Svensson, Harmonic morphisms from even-dimensional hyperbolic spaces, Math. Scand. 92 (2003), 246–260. [C] M. Svensson, Holomorphic foliations, harmonic morphisms and the Walczak formula, J. London Math. Soc. 68 (2003), 781–794. [D] M. Svensson, Harmonic morphisms in Hermitian geometry, J. Reine Angew...
متن کاملOn the Classification of Quadratic Harmonic Morphisms between Euclidean Spaces
We give a classification of quadratic harmonic morphisms between Euclidean spaces (Theorem 2.4) after proving a Rank Lemma. We also find a correspondence between umbilical (Definition 2.7) quadratic harmonic morphisms and Clifford systems. In the case R −→ R, we determine all quadratic harmonic morphisms and show that, up to a constant factor, they are all bi-equivalent (Definition 3.2) to the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998