Spherical Rank Rigidity and Blaschke Manifolds

  title={Spherical Rank Rigidity and Blaschke Manifolds},
  author={Krishnan Shankar and RALF SPATZIER and BURKHARD WILKING},
By the Rauch comparison theorem we know that along any geodesic there cannot be a conjugate point before π. The well known equality discussion implies that for any normal geodesic c : [0, π] → M there exists a spherical Jacobi field i.e., a Jacobi field of the form J(t) = sin(t)E(t) where E is a parallel vector field (see for instance [Chav93, Theorem 2.15]). This latter characterization is analogous to the notions of (upper) Euclidean rank and (upper) hyperbolic rank studied by several people… CONTINUE READING

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Publications referenced by this paper.

Index parity of closed geodesics and rigidity of Hopf fibrations

  • B. Wilking
  • Invent. Math. vol
  • 2001

Riemannian Geometry — a modern introduction

  • I. Chavel
  • Cambridge University Press, Cambride
  • 1993

Riemannian Geometry

  • M. do Carmo
  • Birkhäuser Boston
  • 1992

Strake, Some examples of higher rank manifolds of non-negative curvature

  • M. R. Spatzier
  • Comm. Math. Helv., vol
  • 1990

Spatzier, Manifolds of nonpositive curvature and their buildings, Inst

  • R. K. Burns
  • Hautes Études Sci. Publ. Math., vol
  • 1987

Nonpositively curved manifolds of higher rank

  • W. Ballmann
  • Ann. of Math. (2), vol
  • 1985

Structure of manifolds of nonpositive curvature I

  • W. Ballmann, M. Brin, P. Eberlein
  • Ann. of Math. (2), vol
  • 1985

Closed geodesics on positively curved manifolds

  • W. Ballmann, G. Thorbergsson, W. Ziller
  • Ann. of Math. (2), vol
  • 1982

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