GEOMETRY ON EXOTIC HYPERBOLIC SPACES

  • Kim, In-Kang (Department of Mathematics Korea Advanced Institute of Science of Technology)
  • Published : 1999.03.01

Abstract

In this paper we briefly describe the geometry of the Cayley hyperbolic plane and we show that every uniform lattice in quaternionic space cannot be deformed in the Cayley hyperbolic 2-plane. We also describe the nongeometric bending deformation by developing the theory of the Cartan angular invariant for quaternionic hyperbolic space.

Keywords

References

  1. J. reine angew. Math. v.492 Bending Deformations of complex hyperbolic surfaces B. Apanasov
  2. J. Geom. Anal. v.1 Harmonic mapping of $K\"{a}hler$ manifolds to excerptional hyperbolic spaces J. A. Carlson;L. $Harn\"{a}ndez$
  3. Hyperbolic spaces, Contribution to Analysis (A collection of papers dedicated to Lipman Bers eds. L. Alfors and others) S. S. Chen;L. Greenberg
  4. Geom. Dedicata v.19 no.1 Ausnahmegruppen und Oktavengeometrie Freudenthal, H, Okataven
  5. Complex hyperbolic Geometry W. Goldman
  6. Thesis, U. C. Berkeley Geometric structures on manifolds and the marked length spectrum I. Kim
  7. Ann. of a Math. Stud. v.78 Strong rigidity of locally symmetric spaces G. D. Mostow
  8. Ann. Math. v.129 $M\'{e}triques$ de Cornot-$Carath\'{e}odory$ et $quasiisom\'{e}tries$ des espaces $sym\'{e}triques$ de rang un Pansu, P.
  9. Princeton lecture notes. The geometry and topology of three manifolds W. P. Thurston
  10. Ann. of Math. v.143 Dimension and rigidity of quasi-fuchsian representations C. Yue
  11. Monographs in Mathematics Ergodic theory and semisimple groups R. Zimmer