A correspondence for isometric immersions into product spaces and its applications

作者：Galvez Jose A; Jimenez Asun; Mira Pablo^*

来源：Journal of Geometry and Physics, 2010, 60(11): 1819-1832.

DOI：10.1016/j.geomphys.2010.07.001

• Isometric immersions
• Warped product manifolds
• Semi-Riemannian geometry
• Non-immersion theorems
• Height estimates
• Holomorphic quadratic differentials

We present a correspondence for isometric immersions that are graphs in Riemannian or semi-Riemannian warped product spaces. We use this correspondence to give several existence and non-existence theorems for hypersurfaces in Riemannian or Lorentzian spaces. In the case of surfaces, we obtain further applications regarding height estimates, harmonic representation of surfaces and the existence of holomorphic quadratic differentials in homogeneous and non-homogeneous spaces.

• 出版日期2010-11