Marian Ioan MUNTEANU
Professor Ph. D, Dr. Habil.
Marian Ioan MUNTEANU
Professor Ph. D, Dr. Habil.
Doctoral information *
Research topic // Tema de cercetare
Special type of submanifolds in (semi)-Riemannian manifolds
Short description:
We have in mind two distinct research directions:
I. HARMONIC MAPS WITH POTENTIAL
Magnetic curves, as critical points of the Landau Hall functional, are intensively studied in the last years. Our target is to extend the notion of magnetic curve to maps between Riemannian manifolds, when a magnetic field is defined on the target manifold. In such a way, we define the notion of magnetic map and our objective is to study geometric properties for these magnetic maps. One important example is furnished by vector fields thought as maps from the manifold to its tangent bundle. In case of unit vector fields we get unit magnetic vector fields, as maps from the manifolds to its (unit) tangent sphere bundle.
II. CR-SUBMANIFOLDS
The main objects of this line of research are the CR-submanifolds (in the sense of Bejancu) satisfying certain natural geometric conditions. Some recent results refer to nearly totally geodesic contact CR-submanifolds.
Clase speciale de subvarietati in varietati (semi-) Riemanniene
Descriere:
Se vor avea in vedere doua directii de cercetare:
I. APLICATII ARMONICE CU POTENTIAL
Curbele magnetice, ca puncte critice ale functionalei Landau Hall, sunt intens studiate in ultima perioada. Se urmareste, de asemenea, extinderea notiunii de curba magnetica la aplicatii intre varietati Riemanniene, cand pe codomeniu este prezent un camp magnetic. Apare astfel notiunea de aplicatie magnetica pentru care se vor studia diverse proprietati geometrice remarcabile. Un exemplu important este furnizat de campurile vectoriale gandite ca aplicatii de la o varietate Riemanniana la fibratul sau tangent. Cand campul este unitar, ne restrictionam la fibratul unitar in sfere (cu structura corespunzatoare) si definim notiunea de camp magnetic unitar.
II. SUBVARIETATI CR
Cercetarea va avea ca tema principala studiul subvarietatilor CR care satisfac anumite conditii geometrice naturale. Studii recente se refera la notiunea de subvarietati CR de contact aproape total geodezice (nearly totally geodesic).
STUDENTS:
Marilena Moruz (postdoc)
(October 2020 - September 2022) project n. PN-III-P1-1.1-PD-2019-0253
Simona Luiza Druta-Romaniuc (postdoc)
(October 2010 - February 2013) project n. POSDRU/89/1.5/S/49944
(*) On May 20, 2015, I defended my habilitation thesis entitled:
Recent developments on magnetic curves in (pseudo)-Riemannian manifolds
Atestat de abillitare: OM 4718/11.08.2015
Afiliere la scoala doctorala de matematica: Hotarare Senat n.5 / 24.09.2015