Grupo de pesquisa
Geometria Diferencial
Instituto de Matemática / Universidade Federal do Rio de Janeiro
Grupo de pesquisa
Geometria Diferencial
Instituto de Matemática / Universidade Federal do Rio de Janeiro
Seminário de Geometria da UFRJ
Escrever a geometria@im.ufrj.br para receber os anúncios do seminário e/ou outras questões.
Encontros 2026
June 16, 2026, 3:15 PM, Room C-116
Ernani Ribeiro (UFC)
Rigidity of Compact Quasi-Einstein Manifolds with Boundary
Abstract. It is known from the classical book *Einstein Manifolds* (Besse, 1984) that quasi-Einstein manifolds correspond to the base of a warped product Einstein metric. Another important motivation for studying quasi-Einstein manifolds comes from the work of Bakry and Émery (1985) on diffusion operators, which is closely related to the theories of smooth metric measure spaces, static spaces, and Ricci solitons. In this talk, we show that a three-dimensional simply connected compact quasi-Einstein manifold with boundary and constant scalar curvature must be isometric either to the standard hemisphere (S^3_+) or to the cylinder (\mathbb{R} \times S^2) with the product metric. In dimension four, we prove that a four-dimensional simply connected compact quasi-Einstein manifold with boundary and constant scalar curvature is isometric either to the standard hemisphere (S^4_+), to the cylinder (I \times S^3) with the product metric, or to the product space (S^2_+ \times S^2) endowed with the product metric. This is joint work with D. Zhou (UFF) and J. Costa (UFPB).
May 26, 2026, 3:15 PM, Room C-116
Ivan Miranda de Almeida (IMPA)
Finite Index CMC Hypersurfaces in Low Dimensions
Abstract. We prove that every complete finite-index immersed CMC hypersurface is either minimal or compact, provided that the ambient six-dimensional manifold is a Riemannian product of a closed manifold with non-negative sectional curvature and a Euclidean factor. This answers affirmatively a question posed by do Carmo for this class of ambient spaces and extends known lower-dimensional results. As a consequence, we complete the classification of two-sided, complete weakly stable CMC hypersurfaces immersed in positively curved space forms in dimension six. We also prove that a complete finite-index CMC hypersurface immersed in hyperbolic six-space with mean curvature (|H| > 7) is compact. This provides a partial answer to a question posed by Chodosh in his ICM survey.
May 19, 2026, 3:15 PM, Room C-116
Yuri Conrado (UFRJ)
Teorema de Batchelor
Abstract. O teorema de Batchelor é um resultado clássico da supergeometria que estabelece uma forma normal para supervariedades suaves. Embora existam diversas demonstrações na literatura, em geral não se enfatiza o caráter geométrico do resultado. Nesta palestra apresentaremos uma demonstração baseada no mapa exponencial de uma conexão, seguindo uma ideia inspirada pela geometria diferencial clássica.
May 5, 2026, 3:15 PM, Room C-116
Rui Loja Fernandes (UI - Urbana Champaign)
Totally Real Fibrations of Complex Manifolds
Abstract. Lagrangian fibrations of symplectic manifolds are abstract versions of integrable systems and play an important role in symplectic geometry, Kähler geometry, mirror symmetry, and related areas. An important class of examples is provided by symplectic toric manifolds. In this talk, I will discuss analogous fibrations in complex geometry, called totally real fibrations, which include the class of complex toric manifolds. One of the main goals of the talk is to explain the connection between such fibrations and log-integral affine manifolds, analogous to the relationship between Lagrangian fibrations and integral affine manifolds. The talk is based on ongoing joint work with Maarten Mol (Toronto) and Daniele Sepe (Medellín).
April 10, 2026, 1:30 PM, Room C-116
Jakob Stein (Unicamp)
Instantons on Dk ALF Gravitational Instantons
Abstract. We discuss ongoing work with Foscolo, Ross, and Sotgiu on the construction of Yang–Mills instantons on noncompact hyperkähler four-manifolds with cubic volume growth of dihedral type, including the Atiyah–Hitchin metric on the moduli space of two monopoles. We focus on the moduli problem near the geometric limit arising from the Sen construction.
March 24, 2026, 3:00 PM, Room C-116
Maria Fernanda Elbert (UFRJ)
Estabilidade de Hipersuperfícies com Curvatura Média de Ordem Superior Constante
Abstract. Nesta palestra discutiremos o conceito de estabilidade para hipersuperfícies com curvatura média de ordem superior constante. Consideraremos os casos de hipersuperfícies compactas, completas e capilares, estabelecendo comparações com a teoria clássica das hipersuperfícies de curvatura média constante.
March 24, 2026, 1:30 PM, Room C-116
Valerio Assenza (IMPA)
Existence and Localization of Closed Magnetic Geodesics with Small Energy
Abstract. One of the classical and most celebrated problems in Hamiltonian dynamics is the existence of periodic orbits on a prescribed energy level. In the context of magnetic dynamics, and adopting a variational approach, this talk presents new results on the existence and localization of low-energy periodic magnetic orbits.A central role is played by the notion of magnetic curvature, recently formalized in full generality in [Ass24, AMRT25]. This work is part of a joint project with Leonardo Macarini and Gabriele Benedetti.