Differential Geometry

Differential Geometry

3 - 9 June, 2012, Będlewo

The conference is planned as the fifth in the series (previous conferences in the years: 2000, 2003, 2005, 2008) of meetings organized in the framework of the BC activities by geometers from the Jagiellonian University in Cracow and Technische Universität Berlin. Since the meeting of the group of researchers from Europe, Japan, China and USA in Oberwolfach in 1986 , they have organized and attended many conferences (in various places of the world) dealing with topics connecting Riemannian (or pseudo-Riemannian) geometry, affine differential geometry (leading the topic far beyond the classical affine differential geometry), PDEs and their geometric aspects. The former conferences essentially enlarged the cooperation between mathematicians representing the above fields as well as attracted young researchers. A detailed list (with references, information about non-published partial results) of open problems was formulated during each of the above mentioned conferences. This time we are going to formulate such a list as well.
A proposed list of topics of the planned meeting contains, in particular, the following:
- manifolds and PDEs (in particular Ricci solitons, geometric solution of the Monge-Ampère equations, solutions for certain types of PDEs via the geometric context in which they arise, nonlinear forth order PDEs which appear when studying curvature problems in affine hypersurface theory)
- affine submanifolds (after some stagnation there have appeared new important papers in the field, for instance two spectacular papers of Z. Hu, C. Lee, H. Li, L. Vrancken, namely complete classification of all Blaschke hypersurfaces with parallel (Levi-Civita) cubic form - in case locally strongly convex (J. Diff. Geom. to appear)- in case of Lorentz metrics (RM to appear),
- relations between submanifolds in the Riemannian and affine settings (parallel submanifolds in the sense of Hicks, Backlund related submanifolds etc.)
- statistical and Hessian manifolds in relation with affine differential geometry
- submanifolds of product spaces (submanifolds with extrinsic symmetry properties, submanifolds solving some variational problems etc.)
- affine geometry on abstract manifolds, in particular the theory of homogeneous affine connections, affine manifolds (in the sense of Auslander),
- Weyl geometries
- manifolds with special structures (Sasakian, Kaehler-Norden, contact etc.)
- curvature conditions (in particular, decomposition of curvature tensor)
- Lagrangian and CR submanifolds (in Riemannian and affine setting)
conditions in Riemannian and pseudo-Riemannian geometry)
- Lagrangian and CR submanifolds (metric and affine)

Organizing Committee

  • Barbara Opozda (Jagiellonian University, Cracow)
  • Udo Simon (Technical University, Berlin)

Programme

Participants

  • Balcerzak Bogdan
  • Banchoff Thomas
  • Borowka Aleksandra
  • Deszcz Ryszard
  • Dillen Franki
  • Djoric Mirjana
  • Drach Kostiantyn
  • Stanisław Ewert-Krzemieniewski
  • Daniel Fox
  • Głogowska Małgorzata
  • Hildebrand Roland
  • Hotloś Marian
  • Hu Zejun
  • Jaiswal Jaiprakash
  • Knöppel Felix
  • Kowalski Oldrich
  • Li Xingxiao
  • Luzynczyk Magdalena
  • Martinez Naveira Antonio
  • Medvedev Alexandr
  • Min Xiong
  • Nikčević Stana
  • Oliker Vladimir
  • Olszak Zbigniew
  • Olszak Karina
  • Opozda Barbara
  • Antoni Pierzchalski
  • Robaszewska Maria
  • Zerrin Şentürk
  • Simon Udo
  • Szancer Zuzanna
  • Wang Changping
  • Wełyczko Joanna
  • Paweł Witowicz
  • Wood John C
  • Xin Yuanlong

Abstracts