Differential Geometry Seminar (2012)
As a project of OCAMI, we shall promote the seminar on differential geometry in the wide sense of including the areas related to geometric analysis, topology, algebraic geometry, mathematical physics, integrable systems, information sciences etc.
| Contact | Yoshihiro Ohnita Shin Kato Department of Mathematics Osaka City University Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, JAPAN |
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| TEL | 06-6605-2617 (Ohnita) 06-6605-2616 (Kato) |
| ohnita@sci.osaka-cu.ac.jp shinkato@sci.osaka-cu.ac.jp |
| Speaker | Satoshi Ueki (Tohoku University) |
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| Title | Deformations of Isotropic Submanifolds |
| Date | January 16 (Wed.) 2013, 14：40～16：10 |
| Place | Dept. of Mathematics, General Research Bldg., 301 |
| Abstract | As an analogy to the Lagrangian and Hamiltonoian deformations of Lagrangian submanifolds, B.Y. Chen introduced isotropic and exact deformations of isotropic submanifolds. In this talk, we will consider the differences between Hamiltonian and exact deformations of isotropic submanifolds. We will also consider the minimality and stability. |
| Speaker | Atsuhide Mori (OCAMI) |
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| Title | Some geometric aspects of foliation-contact topology |
| Date | December 12 (Wed.) 2012, 14:40～16:10 |
| Place | Dept. of Mathematics, General Research Bldg., 301 |
| Abstract | Contact geometry of the 1-jet space for functions of n variables is for 1st order SPDEs. Here a codimension-1 foliation is the structure of (n+1)-submanifold which is a union of Legendrian submanifolds. However, it is hard to construct a compact example of such submanifold. We detect the difficulty by means of toric geometry of complex affine space, which realizes a Reeb component as non-analytic smooth submanifold. On the other hand, we may regard a contact structure as a perturbation of a codimension-1 foliation. We will reconstruct a Poisson manifold, recently constructed by Yoshihiko Mitsumatsu, by using a certain framework where a codimension-1 foliation inherits the almost contact structure from a contact structure approximating it. The dominated principle of this story comes from asymptotically holomorphic geometry due to Donaldson. >From this point of view, I would like to look into the future of foliation topology. |
| Speaker | Kotaro Kawai (Tohoku University&JSPS DC2) |
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| Title | Construction of coassociative submanifolds |
| Date | October 30 (The.) 2012, 17：00～18：30 |
| Place | Dept. of Mathematics, General Research Bldg., 301 |
| Abstract | The notion of coassociative submanifolds is defined as the special class of the minimal submanifolds in G_2 manifolds. In this talk, we introduce the method to construct coassociative submanifolds by using the symmetry of the Lie group action. As an application, we give explicit examples in the 7-dimensional Euclidean space and in the anti-self-dual bundle over the 4-sphere. |
| Speaker | Toru Kajigaya (Tohoku University&JSPS DC2) |
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| Title | On L-minimal Legendrian submanifolds in Sasakian manifolds. |
| Date | October 17 (Wed.) 2012, 14：40～16：10 |
| Place | Dept. of Mathematics, General Research Bldg., 301 |
| Abstract | In Kahler manifolds, there is a notion of Hamiltonian-minimal Lagrangian submanifolds. Corresponding to this notion, we define the notion of L-minimal Legendrian submanifolds in Sasakian manifolds, and investigate the stability. In particular, we determine the stability of L-minimal Legendrian curves in 3-dim Sasakian space forms, and prove the L-unstablity theorem for L-minimal Legendrian submanifolds in the unit sphere. |
| Speaker | Takahiro NODA （Nagoya University & OCAMI） |
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| Title | On Cartan-Kahler theorem |
| Date | October 10 (Wed.) 2012, 14：40～16：10 |
| Place | Dept. of Mathematics, General Research Bldg., 301 |
| Abstract | We can give Cartan-Kahler theorem as one of the important results given in geometry of differential systems. This theorem can be regarded as geometric theory related to the exsistence of local solutions for differential equations. In this talk, I introduce this theory and applications into some geometric problem. |
| Speaker | Ryoichi Kobayashi (Nagoya University) |
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| Title | Hamiltonian volume minimizing property of $U(1)^n$-orbits in $P^n$ |
| Date | July 13 (Fri.) 2012, 16：30～18：00 |
| Place | Dept. of Mathematics, General Research Bldg., 301 |
| Abstract | I will introduce a micro-local technique to study the volume of Hamiltonian deformation of $U(1)^n$ orbits in $P^n(C)$. The idea is to replace a given $U(1)^n$-orbit (resp. its Hamiltonian deformation) by collections of moment tori satisfying certain Bohr-Sommerfeld conditions (resp. their Hamiltonian deformations) and look at the projective embeddings defined by the corresponding "Legendrian distributions". If I have time, I will introduce another approach to the same problem, which is based on "Hamiltonian" mean curvature flow. |
| Speaker | Toshihiro Shoda (Saga University) |
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| Title | On Morse index of minimal surfaces |
| Date | June 15 (Fri.) 2012, 16:30～18:00 |
| Place | Dept. of Mathematics, General Research Bldg., 301 |
| Abstract | Morse index suggests a gap between a given minimal surface and the area minimizing surface in terms of Analysis. It is important subject, but there are few results for this 20 years. This time, we calculated Morse index of the classical minimal surfaces. So I would like to show an outline of that. It is joint work with Professor Norio Ejiri, Meijo University. |
| Speaker | Kentaro Saji (Kobe University) |
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| Title | Surfaces swept by constant curvature curves in the hyperbolic space and their singularities |
| Date | June 13 (Wed.) 2012, 14:40～16:10 |
| Place | Dept. of Mathematics, General Research Bldg., 301 |
| Abstract | Ruled surfaces are one-parameter families of a line in the Euclidean space. One can consider surfaces of one-parameter families of an equidistant curve in the hyperbolic space. In this talk, I shall talk about geometries and singularities of these surfaces. |