Biharmonic surfaces in three-dimensional Riemannian manifolds

• Grant number: 15/00692-5
• Support Opportunities: Regular Research Grants
• Start date: June 01, 2015
• End date: May 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Irene Ignazia Onnis
• Grantee: Irene Ignazia Onnis
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The goals of the present research project are: 1) To give the classification of the biharmonic surfaces of constant mean curvature in the product spaces of a surface with the real line. 2) To determine examples of totally biharmonic surfaces in 3-manifolds with non-constant sectional curvature. 3) To give an answer to the following question: Is it true that the only manifolds that admit totally biharmonic surfaces are the space forms? (AU)

Scientific publications

(4)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

CINTRA, ADRIANA A.; ONNIS, IRENE I.. Enneper representation of minimal surfaces in the three-dimensional Lorentz-Minkowski space. Annali di Matematica Pura ed Applicata, v. 197, n. 1, p. 21-39, FEB 2018. (15/00692-5)

CINTRA, ADRIANA A.; MERCURI, FRANCESCO; ONNIS, IRENE I.. Minimal surfaces in Lorentzian Heisenberg group and Damek-Ricci spaces via the Weierstrass representation. JOURNAL OF GEOMETRY AND PHYSICS, v. 121, p. 396-412, NOV 2017. (15/00692-5)

MONTALDO, STEFANO; ONNIS, IRENE I.; PASSAMANI, APOENA PASSOS. Biconservative surfaces in BCV-spaces. Mathematische Nachrichten, v. 290, n. 16, p. 2661-2672, NOV 2017. (15/00692-5)

ONNIS, IRENE I.; PIU, PAOLA. Constant angle surfaces in the Lorentzian Heisenberg group. ARCHIV DER MATHEMATIK, v. 109, n. 6, p. 575-589, DEC 2017. (15/00692-5)