Research on Differential Geometry of Submanifolds

Principal investigators: Benigno Oliveira Alves

Description

The main interest is the study of singular Finslerian foliations, transnormal functions and isoparametric functions. Part of the Riemannian theory is not generalized to the Finslerian context, so it is important to know what can be generalized, in addition to exploring new events. In this research we explored a very important Finslerian manifold, namely the Randers manifold. These objects are closely related to anisotropic physical issues, for example, the propagation of waves in anisotropic environments, such as forest fires.

Research Projects

• Isoparametric hypersurfaces and isoparametric functions on a Randers manifold.
  Collaborators:   Prof. Benigno Oliveira Alves (UFBA).
  Our goal is to investigate isoparametric hypersurfaces and isoparametric functions in Randers manifold.

• Duality of a singular Finsler foliation
  Collaborators:   Prof. Benigno Oliveira Alves (UFBA) and Prof. Marcos Alexandrino da Silva (USP) .
  Our goal is to generalize Wilking's dualization theorem.

  Our published works

  1. ALEXANDRINO, Marcos M.; ALVES, Benigno O.; JAVALOYES, Miguel Angel. On singular Finsler foliation. Annali di Matematica Pura ed Applicata (1923-), 2019, vol. 198, no 1, p. 205-226.

  2. ALEXANDRINO, Marcos M.; ALVES, Benigno O.; DEHKORDI, Hengameh R. On Finsler transnormal functions. Differential Geometry and its Applications, 2019, vol. 65, p. 93-107.

  3. ALVES, Benigno; JAVALOYES, Miguel. A note on the existence of tubular neighbourhoods on Finsler manifolds and minimization of orthogonal geodesics to a submanifold. Proceedings of the American Mathematical Society, 2019, vol. 147, no 1, p. 369-376.

  Our submitted works

  1. ALEXANDRINO, Marcos M.; ALVES, Benigno; JAVALOYES, Miguel Angel. On equifocal Finsler submanifolds and analytic maps. arXiv preprint arXiv:2102.01257, 2021.

  Our preprints