Biharmonic surfaces in three-dimensional Riemannian manifolds

• Grant number: 15/00692-5
• Support Opportunities: Regular Research Grants
• Duration: June 01, 2015 - 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

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(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.; 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)

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)

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)