Rigidity and Convexity of Hypersurfaces in Spheres

  • M. P. do Carmo
  • F. W. Warner
Chapter

Abstract

We shall consider isometric immersions \(x:{\text M}^{n}\rightarrow\,\,{\text X}^{n+1}\) of a compact, connected, orientable, n-dimensional \((n\geq 2),{\text C}^\infty\) Riemannian manifold \({\text M}^{n}\) in a simply connected Riemannian manifold \({\text X}^{n+1}\) of constant sectional curvature.

Keywords

Riemannian Manifold Convex Body Sectional Curvature Fundamental Form Hyperbolic Space 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • M. P. do Carmo
    • 1
    • 2
    • 3
  • F. W. Warner
    • 1
    • 2
    • 3
  1. 1.University Of CaliforniaBerkeleyUSA
  2. 2.I.M.P.A.Rio de JaneiroBrazil
  3. 3.University Of PennsylvaniaPhiladelphiaUSA

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