Hermitian and Quaternionic Structures on Manifolds and Applications
CNCS grant PNII-ID-PCE-2011-3-0362 contract no. 33/2011
Project description: The project refers to hermitian and quaternionic structures on manifolds, and their connections with the geometry of Frobenius manifolds, harmonic maps and generalized complex geometry. We use methods from real and complex differential geometry, twistor theory and isomonodromic deformations.
Project coordinator
· Dr. Liana David, Scientific Researcher II at Institute of Mathematics "Simion Stoilow" of the Romanian Academy
Research team (in alphabetical order)
Intermediate Evaluation Report: link
First phase of the project (01.01-2012-15.12.2012)
Expected results: Constructions of F-manifolds and related structures;
Scientific report: link
Scientific papers
· D. V. Alekseevsky, L. David: A note about invariant SKT-structures and generalized Kahler structures on flag manifolds, Proc Edinburgh Math Soc, vol. 55, no. 3, 2012, pag. 543-549. DOI: 10.1017/S001309151000101
· G. Baditoiu: Classification of pseudo-Riemannian submersions with totally geodesic fibers from pseudo-hyperbolic spaces, Proc London Math Soc, vol. 105, no 6 (2012) pag. 1315-1338. DOI: 10.1112/plms/pds027
· G. Baditoiu, S. Ianus, A. M. Pastore: Spectral properties of Riemannian Legendre foliations, Bull. Math. Soc. Sci. Math. Roumanie, vol. 56(104), no. 2, 2013, pag. 135-150, link
· L. David: On adding a variable to a Frobenbius manifold and generalizations, Geom Dedicata, vol. 167 (2013), p. 189-214, DOI: 10.1007/s10711-012-9809-y.
· L. David: F-manifolds and eventual identities, Oberwolfach Reports, vol. 9 (2), 2012, p. 1389-1392.
· S. Marchiafava, R. Pantilie: Twistor Theory for co-CR quaternionic manifolds and related structures, Israel J. Math, 195 (2013) p. 347-371, DOI: 10.1007/s11856-013-0001-3.
· S. Marchiafava, R. Pantilie: A note on CR quaternionic maps, Adv. Geom, 13 (4) (2013), p. 605-612, DOI: 10.1515/advgeom-2013-0006.
· R. Pantilie: Generalized quaternionic manifolds, Ann Mat Pura Applic, 193(2014), p. 633-641, DOI:10.1007/s10231-012-0294-6.
Presentations as Invited Speakers
· Liana David: Singularity Theory and Integrable Systems, Oberwolfach (Germany), April 2012.
· Liana David: The Central European Mathematical Seminar, Brno (Czech Republic), December 2012.
· Radu Pantilie: Brest University Seminar, Brest (France), June 2012.
Research Visits Abroad
· Gabriel Baditoiu: The Erwin Schrödinger International Institute for Mathematical Physics (Vienna), June (15 days), 2012.
· Liana David: Institut des Hautes Etudes Scientifiques (Paris), 2 months 2012.
· Liana David: Brno University (Czech Republic), November (10 days) 2012.
· Radu Pantilie: Brest University (France), 3 months 2012.
Second phase of the project (16.12.2012-15.12.2013)
Expected results (according to AAD 2013): 1) CDV-structures and obstructions; 2) Submanifold theory in CDV-manifolds; 3) Foliations in CR-quaternionic geometry.
Scientific report: link
Scientific papers
· L. David, I. A. B. Strachan: Symmetries of F-manifolds with eventual identities and special families of connections, Ann. Sc. Norm. Sup. Pisa, Vol. XIII (2014), issue 3, p. 641-674, DOI: 10.2422/2036-2145.201205_010
· L. David, I. A. B. Strachan: tt* Geometry on the Big Phase Space, Comm. Math. Physics, vol. 329 (1) (2014), p. 295-323, DOI:10.1007/s00200-014-1964-6
· R. Pantilie: On the classification of real vector spaces of a quaternionic vector space, Proc. Edinb. Math Soc, vol. 56, no. 2, pag. 615-622, DOI:10.1017/S0013091513000011.
Presentations as Invited Speakers
· Monica Aprodu: Workshop for Young Researchers in Mathematics, Constanta, Romania, May 2013.
· Gabriel Baditoiu: Workshop for Young Researchers in Mathematics, Constanta, Romania May 2013.
· Radu Pantilie: Aniversary Conference, Faculty of Science – 150 Years, University of Bucharest, Romania, 29 August – 1 September 2013.
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Research Visits Abroad
· Liana David: Brno University (Czech Republic), February (10 days) 2013.
· Radu Pantilie: The University of Rome “La Sapienza”, September (10 days) 2013.
Workshop: The director of the project is a co-organizer of The 11-th International Workshop on Differential Geometry and its Applications – Ploiesti, September 19-22, 2013.
Third phase of the project (16.12.2013-31.12.2014)
Expected results (according to AAD 2014): 1) Riemannian submersions; 2) Differential operators in quaternionic geometry and generalized geometry; 3) Cartan connections in parabolic geometry.
Scientific report: link
Scientific papers
· Monica Aprodu, Marian Aprodu: Holomorphic vector bundles on Kahler manifolds and totally geodesic foliations on Euclidian open domains, Diff. Geom. Applic, 39 (2015) , p. 10-19, DOI:10.1016/j.difgeo.2015.01.002, file, arxiv:1409.3701
· D. Alekseevsky, L. David: Tanaka structures (non-holonomic G-structures) and Cartan connections, ‘Conformal and Complex Geometry’, volume in the Honour of P. Gauduchon, Editors: A. Moroianu, L. Ornea, J. Geom. Physics, vol. 91, p. 88-100, (2015); DOI:10.1016/j.geomphys.2015.01.018; file, arxiv:1409.8405
· L. David: On cotangent manifolds, complex structures and generalized geometry, Ann. Inst. Fourier, vol. 66 (1) (2016), p. 1-28 arxiv:1304.3684
· R. Pantilie: On the twistor space of a (co-)CR quaternionic manifold, New-York J. Math. 20 (2014), p. 959-971, http://www.nyjm.albany.edu/j/2014/20-46v.pdf
· R. Pantilie: On the quaternionic manifolds whose twistor spaces are Fano manifolds, Tohoku Math. J. (2) 67 (2015) p. 507-511, arXiv:1411.2225
Presentations as Invited Speakers at International Workshops
· Gabriel Baditoiu: Real and Complex Differential Geometry, Bucharest (Romania), 8-12 September 2014
· Liana David: Real and Complex Differential Geometry, Bucharest (Romania), 8-12 September 2014.
· Radu Pantilie: The 10th Differential Geometry Day and The Differential Geometry Workshop, Lund (Sweden), 15-16 May 2014.
Foreign visitors:
Prof. Dmitri Alekseevsky from Institute for Information and Transmission Problems, Moscow, visited, as an Invited Professor, the host institution of the project, IMAR. His travel expenses were supported by the budget of the project.
Fourth phase of the project (01.01.2015-30.12.2015)
Expected results: 1) Totally geodesic foliations on open subsets in Euclidian space; 2) Riemannian submersions (continuation of the first objective from 2014); 3) Regular F-manifolds; 4) Harmonic morphisms
Scientific report: link
Scientific papers
· P. Baird, R. Pantilie: On Ricci solitons and twistorial harmonic morphisms, sent for publication, file, arxiv:1210.4688
· L. David, C. Hertling: Regular F-manifolds: initial conditions and Frobenius metrics, accepted in Ann. Sc. Norm. Sup. Pisa, file, arXiv:1411.4553
Presentations as Invited Speakers
· Liana David, Geometry and PDE’s, Timisoara (Romania), 29-30 May 2015.
· Radu Pantilie, Harmonic maps, biharmonic maps, harmonic morphisms and related topics, Calgari (Italy), 9-13 June 2015.
· Liana David, University of Hamburg Research Seminar, Hamburg (Germany), 11 November 2015
Other participations at conferences
· Monica Aprodu participated at The 8th Congress of Romanian Mathematicians, Iasi, June 2015 and at Workshop for Young Researchers in Mathematics, Constanta, May 2015.
Research visits abroad
· Gabriel Baditoiu, The interrelation between mathematical physics, number theory, and noncommutative geometry, Erwin Schrodinger International Institute for Mathematical Physics, Vienna (Austria), 1-14 March 2015
Foreign visitors:
Prof. Ian Strachan from University of Glasgow (Great Britain), visited, as an Invited Professor, the host institution of the project, IMAR. His travel and local expenses were supported by the budget of the project.
Fourth phase of the project (31.12.2015-30.12.2016)
Expected results: 1) Compatible structures on regular F-manifolds (applications of the Objective 'Regular F-manifolds' from 2015); 2) The geometry of stratifolds, 3) Cartan connections in parabolic geometry (continuation of Objective 3 from 2014)
Scientific report: link
Scientific papers
· M. A. Aprodu: On the exponential map on Riemannian polyhedra, sent for publication
· D. V. Alekseevsky, L. David: Prolongation of Tanaka structures: an alternative approach, accepted in Annali di Matematica Pura ed Applicata, link
· G. Baditoiu: Classification of homogeneous Einstein metrics on pseudo-hyperbolic spaces, sent for publication
· M. Benyounes, E. Loubeau, R. Pantilie: Harmonic morphisms and moment maps on hyper-Kahler manifolds, accepted in Manuscripta Math. DOI: 10.1007/s00229-016-0894-3
· L. David C. Hertling: Hermitian metrics on F-manifolds, J. Geom. Physics, 107 (2016), p. 60-78, link
· R. Pantilie: Quaternionic-like manifolds and Homogeneous Twistor Spaces, accepted in Proc. Royal Soc. A. link
Presentations as Invited Speakers
· Gabriel Baditoiu, Workshop for Young Researchers in Mathematics, Constanta (Romania), May 2016.
· Liana David, Geometric Structures related to Hermitian and almost-Hermitian manifolds, Hannover (Germany), May 2016.
Other participations at conferences
· Monica Aprodu participated at Workshop for Young Researchers in Mathematics (Constanta, Romania), May 2016.
· Gabriel Baditoiu participated at The XXIVth International Conference on Integrable Systems and Quantum Symmetries (Prague, Czech Republic) June 2016.
Research visits abroad
Liana David visited University of Hamburg (Germany)
Radu Pantilie visited University of Ferrara (Italy)
Foreign visitors:
Prof. Claus Hertling (University of Mannheim, Germany) and Prof. Andrei Moroianu (CNRS France) visited the host institution of the project, IMAR, for collaboration on the topics of the project. They gave a presentation of their research.