Real hypersurfaces with constant principal curvatures in the complex hyperbolic plane
We classify all real hypersurfaces with constant principal curvatures in the complex hyperbolic plane.
math.DG↗
arXiv subjects
Jurgen Berndt
Publications and source records attributed to Jurgen Berndt.
Real hypersurfaces with constant principal curvatures in complex hyperbolic spaces
We classify all real hypersurfaces with three distinct constant principal curvatures in complex hyperbolic spaces of dimension greater than two.
math.DG↗
Cohomogeneity one actions on noncompact symmetric spaces of rank one
We classify, up to orbit equivalence, all cohomogeneity one actions on the hyperbolic planes over the complex, quaternionic and Cayley numbers, and on the complex hyperbolic spaces of dimension greater than two. For the quaternionic hyperbolic spaces of dimension greater than two we reduce the classification problem to a problem in quaternionic linear algebra and obtain partial results. For real hyperbolic spaces, this classification problem was essentially solved by Elie Cartan.
math.DG↗
Projective planes, Severi varieties and spheres
A classical result asserts that the complex projective plane modulo complex conjugation is the 4-dimensional sphere. We generalize this result in two directions by considering the projective planes over the normed real division algebras and by considering the complexifications of these four projective planes.
math.DG↗