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Mediterranean Journal of Mathematics

, Volume 12, Issue 1, pp 173–185 | Cite as

Normal Bundles of Surfaces in Riemannian Manifolds

  • Lei Sun
  • Zhong-Hua Hou
Article
  • 123 Downloads

Abstract

Let f : SM n be an immersed surface in a Riemannian manifold M. Let NS be the normal bundle of S in M and TM be the tangent bundle of M. Let F : (NS, g a,b ) → (TM, G a,b ) be the natural isometric immersion induced by f with g a,b  = F * G a,b , where G a,b is the Cheeger–Gromoll type metric on TM. In this paper, we study the extrinsic geometric properties of NS in (TM, G a,b ) in terms of properties of the immersion f. In particular, the conditions of minimality and constant mean curvature are studied.

Mathematics Subject Classification (2000)

90C33 90C30 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Institute of MathematicsDalian University of TechnologyDalianChina

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