Research project PN-II-RU-TE-2014-4-0004, 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
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 3-dimensional spaces.
O3. Study of biharmonic and biconservative submanifolds in product spaces Mn(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 proper-biharmonic surfaces of constant Gaussian curvature in spheres, J. Math. Soc. Japan 68 (2016), 997–1024.
2. S. L. Druta-Romaniuc, 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 3-dimensional space forms, Comm. Anal. Geom. 24 (2016), 1027 - 1045.
5. M. I. Munteanu, A. I. Nistor, On some closed magnetic curves on a 3-torus, 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 quasi-Sasakian 3-manifolds, 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 2-4 June 2016, to appear.
1. D. Fetcu, A. L. Pinheiro, Biharmonic Submanifolds in Riemannian Manifolds, Demiurg Publishing House, Iasi, Romania, 2016, 90 pp. (ISBN 978-973-152-337-8) (in Romanian), EDUFBA, Salvador, Brazil, to appear (in Portuguese).
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.