Annals of the University of Bucharest (Mathematical Series)

Titlul proiectului: PROBLEME RECENTE IN TEORIA SUBVARIETATILOR

Tipul proiectului: Proiecte de cercetare pentru tineri cercetatori

Echipa de cercetare a FMI este formata din:

Director de proiect:
Asist.dr. Adela Mihai

Assist.prof.dr. Bogdan Suceava ()
Prep.drd. Valentin Ghisoiu
Drd. Simona Decu ()

Tema face parte din Programul National de Cercetare de Excelenta (CEEX 2005) Modulul II - Proiecte de Dezvoltare a Resurselor Umane pentru Cercetare.

Teoria invariantilor Chen a fost initiata de B.-Y. Chen in 1993. Prima inegalitate a lui Chen furnizeaza o noua conditie necesara ca o varietate riemanniana sa admita o imersie minimala intr-un spatiu euclidian. Ulterior, el a introdus "Δ"-invariantii, cunoscuti azi ca invariantii Chen si a demonstrat inegalitati optime pentru acestia (invarianti intrinseci) in functie de principalul invariant extrinsec (curbura medie).

Mai tarziu s-au obtinut inegalitati de tip Chen si pentru alti invarianti intrinseci, de exemplu: curbura scalara, curbura Ricci, etc.. Aceasta teorie a cunoscut o larga dezvoltare in Belgia, Brazilia, Franta, Japonia, Polonia, Romania, SUA, etc..

Ne propunem sa gasim noi aplicatii ale inegalitatilor lui Chen, in particular obstructii topologice si diferentiale la diverse clase de subvarietati in forme spatiale complexe si respectiv Sasaki.

De asemenea vom construi invarianti specifici pentru anumite clase de spatii Riemann, vom obtine estimari optime ale acestora in functie de curbura medie si vom investiga cazul de egalitate.

In particular, vom continua studiul produselor warped in forme spatiale reale si complexe si avem in vedere demonstrarea de inegalitati optime intre invarianti intrinseci (ca de exemplu functia warping) si invarianti extrinseci.

Pentru ca studiul subvarietatilor puternic minimale in forme spatiale complexe sa fie complet, este important sa furnizam noi exemple de hipersuprafete complexe ce satisfac global conditia de minimalitate puternica. In prezent nu exista nici un articol dedicat acestui concept in generalitatea sa. Constructia unor astfel de hipersuprafete de dimensiune mai mare sau egala cu 3 este un alt obiectiv al acestui proiect.

Annals of the University of Bucharest (mathematical series), ISSN 2067-9009 is a mathematical research journal, published by the University of Bucharest, Faculty of Mathematics and Computer Science. This journal continues Analele Universitatii din Bucuresti-Matematica, founded in 1952. Annals of the University of Bucharest (mathematical series) aims at publishing high level original research papers and surveys, in all areas of pure and applied mathematics. The papers published in this journal are abstracted in Mathematical Reviews and Zentralblatt Math. The journal consists of one yearly volume divided in 2 issues. Contributions should be in English and should be sent to one of the members of the Editorial Board or to one of the Editorial Secretaries.

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EDITORIAL OFFICE

FACULTY of MATHEMATICS and COMPUTER SCIENCE
UNIVERSITY of BUCHAREST
Str. Academiei 14
010014 Bucharest, Romania

Contact: annalsub fmi.unibuc.ro

ISSN 2067-9009

EDITORIAL BOARD

CABIRIA ANDREIAN-CAZACU (University of Bucharest, Cabiria.Andreian@imar.ro) • VIOREL BARBU (University of Iasi, vb41@uaic.ro) • LUCIAN BEZNEA ("Simion Stoilow" Inst.of Math., Lucian.Beznea@imar.ro) • HAIM BREZIS (The State University of New Jersey, brezis@math.rutgers.edu) • STEFAAN CAENEPEEL (Vrije Universiteit Brussel, scaenepe@vub.ac.be) • ION CHITESCU (University of Bucharest, ionchitescu@yahoo.com) • PHILIPPE CIARLET (City University of Hong Kong, MAPGC@cityu.edu.hk) • DOINA CIORANESCU (Universite Pierre et Marie Curie, cioran@ann.jussieu.fr) • NICOLAIE D. CRISTESCU (University of Bucharest, cristesc@ufl.edu) • ROMULUS CRISTESCU (University of Bucharest, romuluscristescu@yahoo.com) • IOAN CUCULESCU (University of Bucharest, icucul@fmi.unibuc.ro) • NICOLAE DINCULEANU (University of Florida, nd@math.ufl.edu) • VIOREL IFTIMIE(University of Bucharest, viftimie@fmi.unibuc.ro) • GEORGE GEORGESCU (University of Bucharest, georgescu@fmi.unibuc.ro) • PALTIN IONESCU (University of Bucharest, Paltin.Ionescu@imar.ro) • MARIUS IOSIFESCU ("Gh. Mihoc-C. Iacob" Inst. of Math. Statist. and Appl. Math, miosifes@acad.ro) • YVON MADAY (Universite Pierre et Marie Curie, maday@ann.jussieu.fr) • GERARD MAUGIN (Universite Pierre et Marie Curie, gerard.maugin@upmc.fr) • JEAN MAWHIN (Universite Catholique de Louvain, Jean.Mawhin@uclouvain.be) • PETRU MIRONESCU (Université de Lyon, mironescu@math.univ-lyon1.fr) • CONSTANTIN NASTASESCU (University of Bucharest, constantin_nastasescu@yahoo.com) • LIVIU ORNEA (University of Bucharest, lornea@gta.math.unibuc.ro) • DORIN POPESCU (University of Bucharest, Dorin.Popescu@imar.ro) • VASILE PREDA (University of Bucharest, preda@fmi.unibuc.ro) • ROGER TEMAM (Indiana University, temam@indiana.edu) • IOAN TOMESCU (University of Bucharest, ioan@fmi.unibuc.ro)

EDITOR-IN-CHIEF:
MANAGING EDITOR:

EDITORIAL SECRETARIES:
RADU MICULESCU, University of Bucharest, miculesc@yahoo.com
MIHAI-SORIN STUPARIU, University of Bucharest, stupariu@fmi.unibuc.ro