This project is built around the following central research question: Whenisometric immersions of (intrinsically) homogeneous manifolds in space forms in lowcodimension are orbits of a subgroup of the isometries of the ambient space, that is,extrinsically homogeneous. More precisely, this project aims to apply the recently developed techniquesabout isometric rigidity to study Riemannian manifolds in dimensionsgreater than 2. This project also aims to study homogeneous hypersurfaces in complex space formsand products of space forms, with the same objective, to determine when suchhypersurfaces are extrinsically homogeneous. Although there are not so many resultsabout isometric rigidity in the literature for these ambient spaces, the author intendsto obtain results about isometric rigid similar to the classical ones adapted to this problem, that is, for isometricimmersions that come from intrinsic rigid movements.
News published in Agência FAPESP Newsletter about the scholarship: