Members :

1. Ioan Bucataru - senior researcher

2. Ana Irina Nistor - postdoctoral researcher

3. Marilena Moruz - master student (from January 2013)

2011:

I. Bucataru , Z. Muzsnay: Projective Metrizability and Formal Integrability, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 7 (2011), 114 (22 pages). (IF: 1.243)

2012:

C. Calin, M. Crasmareanu, M.I. Munteanu: Slant curves in three-dimensional f-Kenmotsu manifolds , J. Math. Anal. Appl. 394 (2012) 400–407. ( IF: 1.050)

I. Bucataru , M.F. Dahl: k-Parameter geodesic variations, Journal of Geometry and Physics 62 (2012) 2121-2132. ( IF: 1.055 )

C. Calin, M. Crasmareanu, M.I. Munteanu, V. Saltarelli: Semi-invariant ξ ^ -submanifolds of generalized quasi-Sasakian manifold , Taiwan. J. Math. 16 (2012) 6, 2053-2062. (IF: 0.670)

I. Bucataru, Z. Muzsnay: Projective and Finsler metrizability: parameterization-rigidity of the geodesics, International J. Math. 23 (2012) 9, 1250099 (15 pages). (IF: 0.559) 

2013:

S.L. Druta Romaniuc, M.I. Munteanu: Killing magnetic curves in a Minkowski 3-space, Nonlinear Analysis: Real World Applications 14 (2013) 383–396. (IF: 2.201)

B.Y. Chen, M.I. Munteanu: Biharmonic ideal hypersurfaces in Euclidean spaces, Diff. Geom. Appl. 31 (2013) 1, 1-16.
(IF: 0.484)

I. Bucataru, Z. Muzsnay: Sprays metrizable by Finsler functions of constant flag curvature, Diff. Geom. Appl. 31 (2013) 3, 405–415. (IF: 0.484)

M. Crasmareanu, C.E. Hretcanu, M.I. Munteanu, Golden- and Product- shaped hypersurfaces in real space forms,
Int. J. Geom. Methods Modern Phys. 10 (2013) 4, art. no. 1320006 (9 pages). (IF: 0.626)

I. Bucataru, A setting for higher order differential equation fields and higher order Lagrange and Finsler spaces, J. Geom. Mech. 5 (2013) 3, 257 - 279. (IF: 1.182)

R. Lopez, A.I. Nistor: Surfaces in Sol₃ space foliated by circles, Results in Mathematics, 64 (2013) 3-4, 319-330.
DOI: 10.1007/s00025-013-0316-8, (IF: 0.508).

M.I. Munteanu : Magnetic curves in the Euclidean space: one example, several approaches, Publications de l'Institut Mathematique, 94 (108) (2013) 2, 141-150. (IF:0.195).

M.I. Munteanu, A.I. Nistor: Magnetic trajectories in a non-flat R⁵ have order 5, Proceedings of the conference Pure and Applied Differential Geometry, PADGE 2012, Eds. J. Van der Veken, I. Van de Woestyne, L. Verstraelen, L. Vrancken, Shaker Verlag Aachen 2013, 224-231. ISBN 978-3-8440-2363-3.

2014:

M.I. Munteanu, L. Vrancken: Minimal contact CR submanifolds in S²ⁿ⁺¹ satisfying the δ(2)-Chen's inequality, J. Geom. Phys. 75 (2014), 92 - 97. (IF: 1.055)

Y. Fu, M.I. Munteanu : Generalized constant ratio surfaces in E³, Bull. Braz. Math. Soc., 45 (2014) 1. (IF: 0.348).

A.I. Nistor : Constant angle surfaces in solvable Lie groups, Kyushu J. Math. (2014), 68 (2014) 2, xx-xx (IF: 0.359)

M.I. Munteanu : The Landau Hall problem on canal surfaces, J. Math. Anal. Appl. 414 (2014) 2, 725-733, (IF: 1.050)

J. Inoguchi, M.I. Munteanu: Magnetic maps, Int. J. Geom. Methods Modern Phys., 11 (2014) 6, art. 1450058, (IF: 0.626).

M.I. Munteanu, A.I. Nistor: A note on magnetic curves on S ²ⁿ⁺¹, Comptes Rendus Mathematiques, 352 (2014) 5, 447 - 449. (IF:0.477) .

2015:

G. Calvaruso, M.I. Munteanu, A. Peronne: Killing magnetic curves on three dimensional almost paracontact manifolds, J. Math. Analysis Appl. accepted (IF: 1.050).

R. Lopez, M. Moruz: Translation and homothetical surfaces in Euclidean space with constant curvature, J. Korean Math. Soc. accepted (IF 0.415).

M. Babaarslan, M.I. Munteanu: Time-like loxodromes on rotational surfaces in Minkowski 3-spaces, An.St. ale Univ.`Al.I.Cuza` din Iasi, DOI: 10.2478/aicu-2013-0021, accepted (IF: 0.188).

Submitted papers:

J. Inoguchi, M.I. Munteanu: Periodic magnetic curves in elliptic Sasakian space forms, submitted.

S.L. Druta-Romaniuc, J. Inoguchi, M.I. Munteanu, A.I. Nistor: Magnetic curves in Sasakian and cosymplectic manifolds, submitted.

M. Moruz, M.I. Munteanu, Minimal translation hypersurfaces in E⁴, submitted.

G. Calvaruso, M.I. Munteanu: Hopf magnetic curves in the anti-de Sitter space H ³₁, submitted.

M.I. Munteanu, O.Palmas, G. Ruiz-Hernandez, Translation submanifolds in Euclidean spaces, in preparation.

N.B. The IFs correspond to year 2012.

2012:

• M.I. Munteanu: 17-th Geometrical Seminar (Zlatibor, Serbia – September 2012)
  (invited speaker); Killing magnetic trajectories in 3-dimensional Riemannian manifolds;
• M.I. Munteanu: Conference PADGE: Pure and Applied Differential Geometry (Leuven, Belgium– August 2012): Biharmonic ideal hypersurfaces in Euclidean spaces;
• M.I. Munteanu : 6-th European Congress of Mathematics (Krakow, Poland – July 2012)
  Award: The best research poster : The classification of Killing magnetic curves in M²(c) x R;
• M.I. Munteanu : X Geometric Symposium (Burhaniye, Balikesir, Turkey– June 2012)
  (invited speaker); Translation surfaces in some homogeneous spaces: minimality;
• M.I. Munteanu: Universidad de Sevilla, Spain, May 2012; (research visit);
• M.I. Munteanu: University of Leuven (KU Leuven), March 2012; (research visit);
• A.I. Nistor: 17-th Geometrical Seminar - participant (Zlatibor, Serbia – September 2012);
• I. Bucataru: University of Santiago de Compostela, Spain, May 2012 (research visit);
• I. Bucataru: 47-th Symposium on Finsler Geometry (Kagoshima, Japan – November 2012):
  Higher order projective metrizability, Finsler and Kawaguchi spaces;
• I. Bucataru: University of Kobe, Japan, November 2012, (research visit).

2013:

• I. Bucataru: University of Ghent, Belgium, January 2013, (research visit);
• A.I. Nistor: University of Leuven, Belgium, February 2013, (research visit);
• A.I. Nistor: Conference RoAIMS - First ROMAI Applied and Industrial Mathematics Symposium, (Iasi -May 2013):
  Magnetic trajectories in a non-flat R⁵ ;
• M.I. Munteanu: University of Belgrade, Serbia, June 2013, (research visit);
• M. Moruz: Transilvania University of Brasov, July 2013, (lessons on Ricci flow);
• M.I. Munteanu: 29-th Brazilian Colloquium of Mathematics, IMPA, (Rio de Janeiro, Brazil - July 2013):
  Reduction results for magnetic curves in Sasakian space forms, (poster);
• M.I. Munteanu: Federal University of Bahia, Salvador, Brazil, August 2013, (research visit);
• M. Moruz: Summer school in Mathematics, University of Perugia, (Perugia, Italy - August 2013);
• M. I. Munteanu: The 13th International Conference of Tensor Society on Differential Geometry and its Applications, and Informatics besides (Iasi-September 2013):
  Reduction results for magnetic trajectories in Sasakian and cosymplectic manifolds (talk)
• M. I. Munteanu: Yamagata University, Yamagata, Japan, September 2013, (research visit);
• M. Moruz: The 11th International Workshop on Differential Geometry and its Applications - participant (Ploiesti - September 2013);
• I. Bucataru: University of Santiago de Compostela, Spain, October 2013, (research visit);
• M. I. Munteanu: Autonomous University of Yucatan (UADY) - National Congress of the Mexican Mathematical Society (SMM) - participant (Merida, Mexico - October 2013) ;
• M. I. Munteanu: National Authonomous University of Mexico (UNAM), Mexico City, Mexico, November 2013, (research visit).

2014:

• M.I. Munteanu: University of Salento, Italy, February 15 - March 7, 2014, (research visit);
• J-Inoguchi (Yamagata University): March 9 - 16, 2014, research visit at University Al.I.Cuza of Iasi;
• M.I. Munteanu: Vrnacka Banja (University of Nis), Serbia, May 24 - 29, 2014, conference XVIII geometrical seminar (talk);
• I. Bucataru: University of Ghent, Belgium, June 2014, (research visit);
• M.I. Munteanu: Daejeon, South Korea, August 7-12, 2014, ICM sattelite conference on Real and Complex submanifolds - participant;
• M.I. Munteanu: Seoul, South Korea, August 13-23, 2014, International Ccongress of Mathematicians (poster);
• I. Bucataru: Technical University of Istanbul, Turkey, September 1-7, 2014, International workshop on finite type submanifolds (talk);
• M. I. Munteanu: Technical University of Istanbul, Turkey, September 1-7, 2014, International workshop on finite type submanifolds (talk);
• A.I. Nistor: University of Cagliari, Italy, September 9-17, 2014, (research visit - partially supported);
• A.I. Nistor: Villasimius, Italy, September 18-21, 2014, conference New Trends in Differential Geometry - participant (partially supported);
• M.I. Munteanu: University of Cagliari, Italy, September 9-17, 2014, (research visit);
• M.I. Munteanu: Villasimius, Italy, September 18-21, 2014, conference New Trends in Differential Geometry - participant;

The study of special type surfaces in homogeneous 3-spaces has known a great development in last years. As well known, Thurston established eight simply connected homogeneous 3D geometries and formulated the famous conjecture saying that every compact 3-manifold admits a canonical decomposition into pieces, each of them carrying one of these geometries. Thurston himself proved a part of this fact which was completed by Perelman. His result motivates a deep study of these simply connected homogeneous Riemannian spaces for a better understanding of them. A good comprehension of such a space is supported by the study of the properties of its submanifolds (curves, surfaces, hypersurfaces). The project we propose is a natural continuation of the research developed by the PI in last 4 years, either by himself or in collaboration with researchers both from Europe and USA. The aim of this project is to investigate some special types of surfaces (e.g. constant angle surfaces, translation surfaces or Weingarten surfaces) as well as to explore magnetic trajectories in certain homogeneous 3-spaces. Geometric characterizations and classification theorems will be given, and part of the obtained results will be extended to higher dimensions. Moreover, other spaces endowed with indefinite metrics will be considered. Last but not least, our purpose is to build a unified research team whose scientific results will have an international relevance in the scientific community.

Objectives :

The exploration of the geometric properties of surfaces embedded in homogeneous spaces of dimension 3 represents a contemporary subject of wide interest. Actually, the study of surfaces in 3-dimensional Thurston geometries has grown considerably in the last decade. Maybe the most important reason is the announced proof of the Thurston geometric conjecture which ensures the dominant role of these spaces among 3D geometries. Fundamental quantities in homogeneous spaces Nil3 and Sol3, such as curvatures, geodesics or holonomy groups, came also recently in attention of mathematicians, but their geometry is far to be completely known. Some other problems arising from physical phenomena may be modeled in these spaces and this aspect makes the study of curves and surfaces in homogeneous spaces (in particular space forms) more attractive.

O1. Constant angle surfaces.
O2. Translation surfaces.
O3. Weingarten surfaces.
O4. Magnetic trajectories in 3-dimensional spaces.

Scientific report 2011-2013 (in Romanian)

Scientific report for the entire period (in Romanian)