12 papers
Codimension one Ricci soliton subgroups of solvable Iwasawa groups
Miguel Dominguez-Vazquez, Victor Sanmartin-Lopez, Hiroshi Tamaru
Recently, Jablonski proved that, to a large extent, a simply connected solvable Lie group endowed with a left-invariant Ricci soliton metric can be isometrically embedded into the…
Existence and uniqueness of inhomogeneous ruled hypersurfaces with shape operator of constant norm in the complex hyperbolic space
Miguel Dominguez-Vazquez, Olga Perez-Barral
We complete the classification of ruled real hypersurfaces with shape operator of constant norm in nonflat complex space forms by showing the existence of a unique inhomogeneous ex…
Homogeneous CR submanifolds of complex hyperbolic spaces
Jose Carlos Diaz-Ramos, Miguel Dominguez-Vazquez, Olga Perez-Barral
We classify homogeneous CR submanifolds in complex hyperbolic spaces arising as orbits of a subgroup of the solvable part of the Iwasawa decomposition of the isometry group of the…
Homogeneous Lagrangian foliations on complex space forms
Jose Carlos Diaz-Ramos, Miguel Dominguez-Vazquez, Takahiro Hashinaga
We classify holomorphic isometric actions on complex space forms all whose orbits are Lagrangian submanifolds, up to orbit equivalence. The only examples are Lagrangian affine subs…
Homogeneous and inhomogeneous isoparametric hypersurfaces in rank one symmetric spaces
Jose Carlos Diaz-Ramos, Miguel Dominguez-Vazquez, Alberto Rodriguez-Vazquez
We conclude the classification of cohomogeneity one actions on symmetric spaces of rank one by classifying cohomogeneity one actions on quaternionic hyperbolic spaces up to orbit e…
Submanifold geometry in symmetric spaces of noncompact type
Jose Carlos Diaz-Ramos, Miguel Dominguez-Vazquez, Victor Sanmartin-Lopez
In this survey article we provide an introduction to submanifold geometry in symmetric spaces of noncompact type. We focus on the construction of examples and the classification pr…