ON MINIMAL LAGRANGIAN SURFACES IN THE PRODUCT OF R... - BV FAPESP
Advanced search
Start date
Betweenand
(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

ON MINIMAL LAGRANGIAN SURFACES IN THE PRODUCT OF RIEMANNIAN TWO MANIFOLDS

Full text
Author(s):
Georgiou, Nikos [1]
Total Authors: 1
Affiliation:
[1] Univ Fed Amazonas, Inst Ciencias Exatas, Manaus, Amazonas - Brazil
Total Affiliations: 1
Document type: Journal article
Source: TOHOKU MATHEMATICAL JOURNAL; v. 67, n. 1, p. 137-152, MAR 2015.
Web of Science Citations: 0
Abstract

Let (Sigma(1), g(1)) and (Sigma(2), g(2)) be connected, complete and orientable 2-dimensional Riemannian manifolds. Consider the two canonical Kahler structures (G(epsilon), J, Omega(epsilon)) on the product 4-manifold Sigma(1) x Sigma(2) given by G(epsilon) = g(1) circle plus g(2), epsilon = +/- 1 and J is the canonical product complex structure. Thus for epsilon = 1 the Kahler metric G(+) is Riemannian while for epsilon = -1, G(-) is of neutral signature. We show that the metric G(epsilon) is locally conformally flat if and only if the Gauss curvatures kappa(g(1)) and kappa(g(2)) are both constants satisfying kappa(g(1)) = -epsilon kappa(g(2)). We also give conditions on the Gauss curvatures for which every G(epsilon)-minimal Lagrangian surface is the product gamma(1) x gamma(2) subset of Sigma(1) x Sigma(2), where gamma(1) and gamma(2) are geodesics of (Sigma(1), g(1)) and (Sigma(2), g(2)), respectively. Finally, we explore the Hamiltonian stability of projected rank one Hamiltonian G(epsilon)-minimal surfaces. (AU)

FAPESP's process: 10/08669-9 - Normal Congruences and Lagrangian submanifolds in spaces of geodesics
Grantee:Nikos Georgiou
Support Opportunities: Scholarships in Brazil - Post-Doctoral