Isometric immersions into 3-dimensional homogeneous manifolds
نویسندگان
چکیده
منابع مشابه
Isometric Immersions into 3-dimensional Homogeneous Manifolds
We give a necessary and sufficient condition for a 2-dimensional Riemannian manifold to be locally isometrically immersed into a 3-dimensional homogeneous manifold with a 4-dimensional isometry group. The condition is expressed in terms of the metric, the second fundamental form, and data arising from an ambient Killing field. This class of 3-manifolds includes in particular the Berger spheres,...
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We give a necessary and sufficient condition for an n-dimensional Riemannian manifold to be isometrically immersed into one of the Lorentzian products Sn×R1 or Hn×R1. This condition is expressed in terms of its first and second fundamental forms, the tangent and normal projections of the vectical vector field. As applications, we give an equivalent condition in a spinorial way and we deduce the...
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We give a spinorial characterization of isometrically immersed surfaces into 3-dimensional homogeneous manifolds with 4-dimensional isometry group in terms of the existence of a particular spinor, called generalized Killing spinor. This generalizes results by T. Friedrich [7] for R3 and B. Morel [16] for S3 and H3. The main argument is the interpretation of the energy-momentum tensor of a genra...
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Assuming minimal regularity assumptions on the data, we revisit the classical problem of finding isometric immersions into the Minkowski spacetime for hypersurfaces of a Lorentzian manifold. Our approach encompasses metrics having Sobolev regularity and Riemann curvature defined in the distributional sense, only. It applies to timelike, spacelike, or null hypersurfaces with arbitrary signature ...
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ژورنال
عنوان ژورنال: Commentarii Mathematici Helvetici
سال: 2007
ISSN: 0010-2571
DOI: 10.4171/cmh/86