Abstracts
Ana Péon Nieto (University of Santiago de Compostela, Spain)
Title:
Abstract:
Catarina Faustino (University of Minho, Portugal)
Title:
Abstract:
Sandro Caeiro Oliveira (University of Vigo, Spain)
Title: Are products of critical metrics also critical?
Abstract: Einstein metrics are the critical metrics for the Hilbert-Einstein functional when restricted to constant volume variations. This functional is determined by the scalar curvature, which is the only scalar curvature invariant of order one. Taking the second-order invariants, the functionals obtained are the so-called quadratic curvature functionals. In the classification of critical homogeneous metrics for quadratic curvature functionals in dimension 4, products of lower-dimensional critical metrics naturally arise. In this talk, we will examine under what conditions this idea can be generalized and the limitations we encounter when working with these products.
Mehmood Ur Rehman (University of Beira Interior, Portugal)
Title: Primitive Immersion of Constant Curvature of Surfaces Into Flag Manifolds
Abstract: Following the seminal result by E. Calabi which establishes the local classification of complex submanifolds with constant holomorphic sectional curvature in complex space forms, several researchers have investigated minimal immersions with constant curvature of Riemann surfaces into symmetric spaces. For isometric immersions, minimality is equivalent to harmonicity, hence the rich theory of harmonic maps becomes highly relevant here. In recent years, the method of harmonic maps has been intensively used to classify such minimal immersions. There exists a well-established theory of twistor constructions of harmonic maps from Riemann surfaces into symmetric spaces. An important class of twistor lifts is that of primitive maps into k-symmetric spaces G/K. For k > 2, primitive maps are harmonic with respect to all G-invariant metrics. Thus, a natural problem arising from these observations is to classify primitive immersions of constant curvature of Riemann surfaces into k-symmetric spaces, when these are equipped with G-invariant metrics. In this talk, I will address this problem. This is a joint work with Rui Pacheco.
