Conformal Actions and Harmonic Morphisms

نویسنده

  • RADU PANTILIE
چکیده

We give necessary and suucient conditions for a conformal foliation locally generated by conformal vector elds to produce harmonic morphisms. Natural constructions of harmonic maps and morphisms are thus obtained. Also we obtain reducibility results for harmonic morphisms induced by (innnitesimal) conformal actions on Einstein manifolds.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Harmonic Morphisms with 1-dim Fibres on 4-dim Einstein Manifolds

Harmonic morphisms are smooth maps between Riemannian manifolds which preserve Laplace's equation. They are characterised as harmonic maps which are horizontally weakly conformal 14, 20]. R.L. Bryant 7] proved that there are precisely two types of harmonic morphisms with one-dimensional bres which can be deened on a constant curvature space of dimension at least four. Here we prove that, on an ...

متن کامل

Harmonic 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 کامل

Harmonic Morphisms with One-dimensional Fibres

We study harmonic morphisms by placing them into the context of conformal foli-ations. Most of the results we obtain hold for bres of dimension one and codomains of dimension not equal to two. We consider foliations which produce harmonic mor-phisms on both compact and noncompact Riemannian manifolds. By using integral formulae, we prove an extension to one-dimensional foliations which produce ...

متن کامل

Harmonic Morphisms on Heaven Spaces

We prove that any (real or complex) analytic horizontally conformal submersion from a three-dimensional conformal manifold (M, cM ) to a twodimensional conformal manifold (N, cN ) can be, locally, ‘extended’ to a unique harmonic morphism from the H(eaven)-space (H, g) of (M, cN ) to (N, cN ). Moreover, any positive harmonic morphism with two-dimensional fibres from (H, g) is obtained this way.

متن کامل

Harmonic morphisms and shear-free ray congruences

We describe the relationship between complex-valued harmonic morphisms from Minkowski 4-space and the shear-free ray congruences of mathematical physics. Then we show how a horizontally conformal submersion on a domain of R 3 gives the boundary values at infinity of a complex-valued harmonic morphism on hyperbolic 4-space.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1999