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The study of the vector field problem for homogeneous spaces

Grant number: 20/00814-1
Support type:Scholarships in Brazil - Master
Effective date (Start): July 01, 2020
Effective date (End): December 31, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Alice Kimie Miwa Libardi
Grantee:Matheus Eduardo Dametto Silva
Home Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
Associated research grant:16/24707-4 - Algebraic, geometric and differential topology, AP.TEM

Abstract

Let M be a smooth connected Hausdorff manifold of dimension n. We denote by TpM the tangent space of M, in p of M, by tauM the fibre bundle of M and by TM , the total space of such fibre bundle. A vector field is a continuous map M to TpM which associates to each point p of M, a vector v(p) in TpM. Then a vector field is a section v : M to TpM. Sankaran presents a very interesting survey on the vector field problem, more specifically on homogeneous spaces. This problem consists on the determination of the maximum number, called span of M, such that there exist vector fields v1, v2, · · · , vr in M such that v1(p), v2(p), · · · , vr(p) in TpM are linearly independent for all p in M. The objective of this project is to study this case to obtain a generalization for other types of spaces. The student intends to do an internship at University of Warmia and Mazury in Poland, under the supervision of Marek Golasinsiki from 2021 January until March. (AU)

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