Biharmonic submanifolds in three dimensional homogeneous manifolds

Author(s)

Apoenã Passos Passamani

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2011-04-14

Examining board members

Irene Ignazia Onnis; Stefano Montaldo; Barbara Corominas Valerio

• Advisor: Irene Ignazia Onnis

Abstract

In this work we study some important results about the theory of the biharmonic submanifolds of tridimensional homogeneous spaces. There exist three classes of simply connected tridimensional homogeneous spaces depending on the dimension of the group of isometries, which can be: 3, 4 or 6. In the case of dimension 6, M will be a space form; if the dimension of the group of isometries is 4, M will be isometric to: either \'H IND. 3\' (Heisenbergs group), or SU(2) (special unitary group), or ~SL(2,R) (universal recovering of the special linear group), or the product spaces \'S POT. 2\' × R and \'H POT. 2\' × R. Except for \'H POT. 3\', in the case of dimension 4 or 6 the homogeneous space is locally isometric to (a part of) \'R POT. 3\', endowed with a metric that depends on two real parameters. Such family of metrics first appears in the work [3] of L. Bianchi and later in the articles [14, 35] of ´E. Cartan and G. Vranceanu, respectively. In this master thesis, we want to study (essentially) results of existence and classification of bi-harmonic submanifolds in these spaces, also known as Bianchi-Cartan-Vranceanus manifolds (AU)

• FAPESP's process: 09/04258-7 - Biharmonic submanifolds in three dimensional homogeneous manifolds
• Grantee: Apoenã Passos Passamani
• Support Opportunities: Scholarships in Brazil - Master