Research project
PNIIRUTE201440004, 272/01.10.2015
a grant of the Romanian National Authority for Scientific Research, CNCS  UEFISCDI
Director: Professor Dorel Fetcu

CONSTANT MEAN CURVATURE AND BIHARMONIC SUBMANIFOLDS
Nr. 272/01.10.2015
Abstract: Submanifolds with constant mean curvature (CMC submanifolds) and, more generally, submanifolds with mean curvature vector field parallel in
the normal bundle (PMC submanifolds) are two of the most studied objects in modern Differential Geometry. A more recent subject is represented by
biharmonic immersions (biharmonic submanifolds), a particular case of biharmonic maps between Riemannian manifolds. The biharmonic maps were
suggested by J. Eells and J. H. Sampson as a natural generalization of harmonic maps and, therefore, biharmonic submanifolds generalize the
classical minimal submanifolds. The aim of our project is to study CMC, PMC, and biharmonic submanifolds in various geometric contexts. New
examples, as well as characterization and classification results, will be obtained. Classical instruments often involved in this kind of studies,
like, for example, holomorphic differentials or Simons type equations, will be used and also new methods will be developed in order to understand
and describe the geometry of such submanifolds.
O1.
Study of submanifolds with parallel mean curvature vector field in Riemannian manifolds.
O2.
Study of biharmonic and biconservative submanifolds in certain 3dimensional spaces.
O3.
Study of biharmonic and biconservative submanifolds in product spaces M^{n}(C)x R.
O4.
Study of biharmonic and biconservative surfaces in complex space forms.
O5.
Study of equivariant biharmonic maps.
O6.
Study of magnetic curves in product spaces.
O7.
Edit a monograph on biharmonic submanifolds.
ISI published papers
1.
E. Loubeau, C. Oniciuc, Constant mean curvature properbiharmonic surfaces of
constant Gaussian curvature in spheres, J. Math. Soc. Japan 68 (2016), 997–1024.
2.
S. L. DrutaRomaniuc, J. I. Inoguchi, M. Munteanu, and A. I. Nistor, Magnetic curves in
cosymplectic manifolds, Rep. Math. Phys. 78 (2016), 33 – 48.
3.
S. Nistor, Complete biconservative surfaces in R^3 and S^3, J. Geom. Phys. 110 (2016), 130 –
153.
4.
D. Fetcu, S. Nistor, and C. Oniciuc, On biconservative surfaces in
3dimensional space forms, Comm. Anal. Geom. 24 (2016), 1027  1045.
5.
M. I. Munteanu, A. I. Nistor, On some closed magnetic curves on a 3torus,
Math. Phys. Anal. Geom. 20 (2017) 2, art. 8.
BDI published papers 1.
S. Montaldo, C. Oniciuc, and A. Ratto, Reduction methods for the bienergy, Rev. Roumaine
Math. Pures Appl. 61 (2016), 261 – 292.
Accepted papers (ISI)
1.
D. Fetcu, E. Loubeau, and C. Oniciuc, Biharmonic tori in spheres,
Differential Geom. Appl., to appear.
2.
J. Inoguchi, M. I. Munteanu, and A. I. Nistor, Magnetic curves in
quasiSasakian 3manifolds, Analysis and Mathematical Physics, to appear.
3.
S. Nistor, On biconservative surfaces, Differential Geom. Appl., to appear.
Accepted papers (Proceedings/BDI)
1.
S. Nistor, C. Oniciuc, Global properties of biconservative surfaces in R^3 and S^3, Proceedings
of The International Workshop on Theory of Submanifolds, Istanbul Technical University, Turkey 24 June 2016, to appear.
Textbook
1.
D. Fetcu, A. L. Pinheiro, Biharmonic Submanifolds in Riemannian Manifolds,
Demiurg Publishing House, Iasi, Romania, 2016, 90 pp. (ISBN 9789731523378) (in Romanian), EDUFBA, Salvador, Brazil, to appear
(in Portuguese).
Habilitation Thesis
1.
D. Fetcu, Submanifolds with Parallel Mean Curvature and Biharmonic Submanifolds in
Riemannian Manifolds, www.researchgate.net, DOI: 10.13140/RG.2.2.29610.11204.
Scientific report 2015 (RO);
Scientific report 2015 (EN) 