Research project
PN-II-RU-TE-2011-3-0108, 51/05.10.2011
a grant of the Romanian National Authority for Scientific Research, CNCS - UEFISCDI
Director:
Professor Cezar Oniciuc
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BIHARMONIC
MAPS AND SUBMANIFOLDS IN CERTAIN GEOMETRIC CONTEXTS Nr.
51/05.10.2011 Abstract: A harmonic map between Riemannian manifolds is a critical point for the
energy functional; the Euler-Lagrange equation associated to this functional
is obtained by vanishing the tension field. The biharmonic maps arise in the work of J. Eells and J.H.
Sampson as a natural generalization of harmonic maps. Accordingly, a smooth
map is biharmonic if it is a critical point of the bioenergy functional. In
the case of submanifolds, the biharmonicity
leads to biharmonic submanifolds,
which represent an interesting generalization of the classical minimal
submanifolds. The aim of the present project is to study the biharmonicity in
various geometric contexts. This can be integrated in a wider research
direction, in which new examples of biharmonic maps and new classification
results for biharmonic submanifolds
are anticipated to be obtained. A complementary research direction of the
present project consists in the study, using cohomological methods, of some
topological and algebraic properties of manifolds and submanifolds, in
contexts that may lead to such properties for biharmonic submanifolds.
O1.
Study of biharmonic submanifolds in 7-dimensional Sasakian space forms and in
the complex projective space CP3 O2.
Study of biharmonic submanifolds with additional geometric
properties in spheres O3.
Study of parallel mean curvature vector field submanifolds in
Riemannian manifolds O4.
Study of biharmonic maps in Lie groups O5.
Study of certain biharmonic type equations from the analytic
point of view O6.
Study of direct images of certain cohomological objects by some
classes of morphisms of manifolds O7.
Edit a monograph on biharmonic maps and submanifolds 2014 ISI published papers 1.
E. Loubeau, C. Oniciuc, Biharmonic surfaces of constant mean curvature, Pacific Journal of Mathematics 271 (1), 213-230, 2014 . 2. R. Caddeo, S. Montaldo, C. Oniciuc, P. Piu, Surfaces in 3-dimensional space forms with divergence-free stress-bienergy tensor, Annali di Matematica Pura ed Applicata 193 (2), 529-550, 2014. 3.
J.I. Burgos
Gil, G. Freixas, R. Litcanu, Generalized holomorphic analytic torsion,
J. Eur. Math. Soc. 6 (3), 463-535, 2014, arXiv:1011.3702 ISI accepted papers 1.
S. Montaldo, C. Oniciuc, A. Ratto, Biconservative surfaces, to appear in Journal of Geometric Analysis. 2.
S. Montaldo, C. Oniciuc, A. Ratto, Proper biconservative immersions into the Euclidean space,
to appear in Annali di Matematica Pura ed Applicata. 3.
D. Fetcu, A. L. Pinheiro, Biharmonic surfaces with parallel mean curvature in
complex space forms, to appear in Kyoto Journal of Mathematics arXiv:1303.4279. Preprints 1. E. Loubeau, C. Oniciuc, CMC proper-biharmonic surfaces of constant Gaussian curvature in spheres. 2013 ISI published papers 1. D. Fetcu, C. Oniciuc, H. Rosenberg, Biharmonic Submanifolds with Parallel Mean Curvature in S^n x R, Journal of Geometric Analysis 23 (4) (2013), 2158-2176. arXiv:0911.3244 2.
A. Balmus,
S. Montaldo, C. Oniciuc, Biharmonic PNMC submanifolds in spheres, Arkiv fur Mathematik 51 (2) (2013), 197-221. arXiv:1110.4258 3.
D. Fetcu, H. Rosenberg, On complete
submanifolds with parallel mean curvature in product spaces, Revista Matematica Iberoamericana 29 (4) (2013), 1283-1306.
arXiv:1112.3452 2012 ISI published papers 1.
D. Fetcu, C. Oniciuc, Biharmonic integral C-parallel submanifolds
in 7-dimensional Sasakian space forms, Tohoku
Mathematical Journal 64(2) (2012), 195-222. arXiv:0911.3244 2.
A. Balmus, S. Montaldo, C. Oniciuc, New results toward the classification of biharmonic submanifolds in Sn. An. St. Univ. Ovidius
Constanta, Seria Matematica
20 (2) (2012), 89-114. arXiv:1111.6063 3.
M. Crasmareanu, I. Stoleriu,
Nonholonomic dynamics of second order and the Heisenberg spinning particle, Int. Jnl. Geo. Met. Mod. Phys.,
9 (7) (2012), 1-9. Habilitation Thesis 1.
Cezar Oniciuc, Biharmonic submanifolds in space forms, Habilitation Thesis,
2012. Other 1.
D. Fetcu, Subvariedades
biharmonicas em variedades Riemannianas (Notas
de aula), Universidade Federal da Bahia, Pos-Graduacao em Matematica - Verao 2013, 02 de
Janeiro a 28 de Fevereiro. Scientific report 2011 (RO);
Scientific report 2011 (EN) |
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Last
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