Normal Congruences and Lagrangian submanifolds in spaces of geodesics

• Grant number: 10/08669-9
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: October 01, 2010
• End date: September 30, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Guillermo Antonio Lobos Villagra
• Grantee: Nikos Georgiou
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

O estudo do conjunto L(M) das geodésicas orientadas de uma variedade riemanniana M pode dar informações relevantes sobre a geometria das subvariedades de M. Em particular, L(M) goza de uma estrutura simplética e as subvariedades lagrangeanas de L(M) correspondem às familias de hipersuperfícies paralelas de M. Neste projeto pretendemos (a) estudar as subvariedades mínimias e H-mínimas de L(M), nos casos M=R^3, H^3 e S^n, relacionando-as com as hipersuperfícies subjacentes de M, (b) usar congruências de geodésicas no estudo dos corpos convexos, em particular no problema de Blaschke-Lebesgue.

Scientific publications

(5)

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

GEORGIOU, NIKOS; LOBOS, GUILLERMO A.. On Hamiltonian minimal submanifolds in the space of oriented geodesics in real space forms. ARCHIV DER MATHEMATIK, v. 106, n. 3, p. 285-293, MAR 2016. (10/08669-9)

GEORGIOU, NIKOS; GUILFOYLE, BRENDAN. Marginally trapped surfaces in spaces of oriented geodesics. JOURNAL OF GEOMETRY AND PHYSICS, v. 82, p. 1-12, AUG 2014. (10/08669-9)

ANCIAUX, HENRI; GEORGIOU, NIKOS. Hamiltonian stability of Hamiltonian minimal Lagrangian submanifolds in pseudo- and para-Kahler manifolds. ADVANCES IN GEOMETRY, v. 14, n. 4, p. 587-612, OCT 2014. (10/18752-0, 10/08669-9)

GEORGIOU, NIKOS. Lagrangian immersions in the product of Lorentzian two manifolds. Geometriae Dedicata, v. 178, n. 1, p. 1-13, OCT 2015. (10/08669-9)

GEORGIOU, NIKOS. ON MINIMAL LAGRANGIAN SURFACES IN THE PRODUCT OF RIEMANNIAN TWO MANIFOLDS. TOHOKU MATHEMATICAL JOURNAL, v. 67, n. 1, p. 137-152, MAR 2015. (10/08669-9)