Viviana Jorgelina Del Barco

• Abstract

  The present project focuses on the study of Killing tensors and locally conformally product (LCP) structures on homogeneous manifolds. It explores these mathematical objects' implications in theoretical physics and Riemannian geometry. The main objectives are to investigate Killing tensors in solvable Lie groups and symmetric spaces, and to further understand the structure of LCP manifold…

  Conformal geometry of homogeneous manifolds, AP.R SPRINT

• Abstract

  The present research proposal is aimed at the study of special geometric structures on Lie groups and their compact quotients, when they exist. The general objective of the project is to determine algebraic and topological constraints for a Lie group to carry certaub Riemannian or conformal structures.Different types of geometric structures will be considered on such manifolds, namely, co…

  Aspects of the conformal and Riemannian geometry of Lie groups and their compact quotients., AP.R

• Abstract

  The project aims to establish a new collaboration between the visiting Professor and Professors del Barco and Grama from IMECC. The topics to be addressed include invariant Killing forms and the Kähler-like metric condition in Lie groups and their compact quotients. (AU)

  Geometry of Lie groups: Killing forms and Kähler-like metrics, AV.EXT

• Abstract

  This project aims to support the Responsible Researcher in the development of research in differential geometry, facilitating her inclusion in the Brazilian mathematical community and contributing to maintain, and further strengthen, her collaborations with researchers abroad. It is expected to bring a network of international exchange to the well established relation between FAPESP and U…

  Special invariant metrics on Lie groups and their compact quotients, AP.R

• Abstract

  This research project seeks to investigate the geometry of nilpotent Lie groups and the analytic properties of their compact quotients. Specifically, a primary objective is to elucidate a theorem that establishes conditions for two Riemannian nilmanifolds to be isospectral. This enables the construction of examples of such manifolds and, therefore, the analysis of geometric properties tha…

  Isospectrality of nilmanifolds, BP.MS

• Abstract

  This project aims to understand research techniques in the geometry of pseudo-Riemannian Lie groups that have a left-invariant metric. This can be done by studying the group of isometries of these varieties. The focus is on certain low-dimensional solvable pseudo-Riemannian Lie groups, and on understanding the known results to carry out a possible extension of these results to more genera…

  Isometries of pseudo-Riemannian Lie group, BP.MS

• Abstract

  The present project aims to deepen the student's understanding of the structure of an abstract Lie algebra equipped with an ad-invariant metric. In this regard, the objective is to comprehend the classification of Lie algebras of fixed dimension endowed with this type of function, up to isomorphism. More precisely, the classification will be studied in algebras of dimension up to 4.Additi…

  Classification of Lie algebras endowed with ad-invariant metrics., BP.IC

• Abstract

  The present project aims to study the geometry of Lie groups equipped with left-invariant Riemannian metrics, with special interest on left-invariant Killing symmetric tensors defined on them. More precisely, it is intended that the student reviews recent articles on these topics, which mainly address nilpotent Lie groups. After this study, the extent of the techniques used in these artic…

  Geometry of Riemannian Lie groups, BP.MS

(Only some records are available in English at this moment)

• Abstract

  In addition to exposing the student to the experience of visiting a mathematics research center abroad with high-level researchers from the University of Minho, this project aims to enable the student to acquire specific research techniques in the geometry of pseudo-Riemannian Lie groups as part of his studies with the advisor abroad, who has extensive experience in the topic. More specif…

  Classification of bi-invariant metrics on 4-dimensional Lie groups, BE.EP.MS

• Abstract

  This research project aims to address the decomposability of left-invariant symmetric Killing 2-tensors on 3-dimensional solvable Lie groups. This problem is a natural continuation of the master's project of the candidate, on which it is being studied left-invariant symmetric Killing tensors on Lie Groups endowed with Riemannian metrics. (AU)

  Symmetric killing 2-tensors on riemannian Lie groups, BE.EP.MS

• Abstract

  We propose to investigate the conformal geometry of flag manifolds. Precisely, we focus on Riemannian metrics g on the manifold such that its conformal class contains a metric g_0 with a particular characteristic, such as being Kahler, with holonomy contained in G_2, or relaxations of these two. In some cases we relax the fact of being (globally) conformal and we only require g_0 to be lo…

  Locally conformal geometry on flag manifolds, BE.EP.PD