Ohnita Yoshihiro

写真a

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Title

Professor

Laboratory location

Sugimoto Campus

Degree 【 display / non-display

  • Tohoku University -  Ph.D.

Research Areas 【 display / non-display

Geometry

Research Career 【 display / non-display

  • Research on differential geometric objects such as harmonic maps, minimal submanifolds, constant mean curvature surfaces,gauge-theoretic equations etc. and their moduli spaces

    (Individual) Project Year :

    1980.04
     
     

    Keyword in research subject:  harmonic map, minimal submanifold, integrable system

  • Joint research on geometry, integrable systems and visualization

    (Collaboration in Japan)

    Keyword in research subject:  differential geometry, integrable system, visualization

Association Memberships 【 display / non-display

  • Mathematical Society of Japan

Committee Memberships 【 display / non-display

  • 1999
    -
    2000

    Mathematical Society of Japan   Councilor

Awards & Honors 【 display / non-display

  • Distinguished Paper Award of 2017 ICCM Best Paper Award

    Hui Ma and Yoshihiro Ohnita, Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces, Journal of Differential Geometry, 97 (2014), 275-348.

    2017.12   ICCM

    Winner : Hui Ma, Yoshihiro Ohnita

Current Career 【 display / non-display

  • Osaka City University   Graduate School of Science   Mathematics and Physics Course   Professor  

Career 【 display / non-display

  • 2005
     
     

    Osaka City University  

  • 1998
    -
    2005

    Tokyo Metropolitan University  

  • 1991
    -
    1998

    Tokyo Metropolitan University  

  • 1986
    -
    1991

    Tokyo Metropolitan University  

Graduate School 【 display / non-display

  •  
    -
    1985

    Tohoku University  Graduate School, Division of Natural Science 

Graduating School 【 display / non-display

  •  
    -
    1980

    Ibaraki University   Faculty of Science  

 

Published Papers 【 display / non-display

  • Geometry of R-spaces canonically embedded in K\"ahler C-spaces as Lagrangian submanifolds

    Yoshihiro Ohnita

    Proceedings of the 22nd International Workshop on Differental Geometry of Submanifolds in Symmetric Spaces and Related Problems  22   115 - 132 2019.09  [Invited]

  • Minimal Maslov number of R-spaces canonically embedded in Einstein-Kahler C-spaces

    Ohnita Yoshihiro

    COMPLEX MANIFOLDS  6 ( 1 ) 303 - 319 2019  [Refereed]

    DOI

  • Lagrangian geometry of the Gauss images of isoparametric hypersurfaces in spheres

    Miyaoka Reiko, Ohnita Yoshihiro

    COMPLEX MANIFOLDS  6 ( 1 ) 265 - 278 2019  [Refereed]

    DOI

  • On Floer homology of the Gauss images of isoparametric hypersurfaces

    Yoshihiro Ohnita

    Springer Proceedings in Mathematics & Statistics “Hermitian-Grassmannian Submanifolds”  203   235 - 247 2017  [Refereed]  [Invited]

  • On classification of minimal orbits of the Hermann action satisfying Koike's conditions (Joint work with Minoru Yoshida)

    Yoshihiro Ohnita, Minoru Yoshida

    Proceedings of the 21st International Workshop on Hermitian Symmetric Spaces and Submanifolds and 14th RIRCM-OCAMI Joint Differential Geometry Workshop  21   1 - 15 2017  [Invited]

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Books etc 【 display / non-display

Conference Activities & Talks 【 display / non-display

  • Introduction to Isoparametric Hypersurface Theory

    Yoshihiro Ohnita  [Invited]

    Intensive lectures at Tokto University of Science  2019.09 

  • Minimal Maslov number of R-spaces canonically embedded in Einstein-K\"ahler C-spaces

    Yoshihiro Ohnita  [Invited]

    The 22nd International Workshop on Differential Geometry of Submanifolds in Symmetric Spaces and Related Problems & The 17th RIRCM-OCAMI Joint Differential Geometry Workshop  2019.08 

  • Lagrangian geometry of the Gauss images of isoparametric hypersurfaces

    Yoshihiro Ohnita  [Invited]

    2019 Workshop on the Isoparametric Theory  2019.06 

  • Minimal Maslov number of R-spaces canonically embedded in Einstein-K\"ahler C-spaces

    Yoshihiro Ohnita  [Invited]

    Conference "Variational problems and the geometry of submanifolds"  2019.05 

  • Minimal Maslov number of R-spaces canonically embedded in Einstein-Kaehler C-spaces

    Yoshihiro Ohnita  [Invited]

    The 2nd International Conference "Geometry of Submanifolds and Integrable Systems", The 16th OCAMI-RIRCM Joint Differential Geometry Workshop & The 4th OCAMI-KOBE-WASEDA Joint International Workshop on Differential Geometry and Integrable Systems  2019.03 

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Grant-in-Aid for Scientific Research 【 display / non-display

  • Deepening and Evolution of Theory of Submanifolds and Harmonic Maps in Symmetric Spaces

    Project/Area Number : 18K03307  Grant-in-Aid for Scientific Research(C) Representative

    Project Year :

    2018.04
    -
    2021.03
     

  • New Development of Submanifold Geometry and Harmonic Map Theory in Symmetric Spaces

    Project/Area Number : 15K04851  Grant-in-Aid for Scientific Research(C) Representative

    Project Year :

    2015.04
    -
    2018.03
     

  • Research on submanifold geometry and harmonic map theory in symmetric spaces

    Project/Area Number : 24540090  Grant-in-Aid for Scientific Research(C) Representative

    Project Year :

    2012.04
    -
    2015.03
     

    Partaker : KATO Shin, SAKAI Takashi, GUEST Martin, KOIKE Naoyuki, TANAKA Makiko S.

     View Summary

    In this project, from the viewpoints of geometric variational problems, integrable systems, Lie theory, symplectic geometry, we promoted to study harmonic maps in symmetric spaces and integrable systems, Hamiltonian stability of Lagrangian submanifolds, minimal submanifold theory, Lagrangian submanifolds related to isoparametric hypersurfaces, isoparametric submanifolds of finite and infinite dimensions. Especially, we has published our results on the property and structure of compact minimal Lagrangian submanifolds embedded in complex hyperquadrics obtained as the Gauss images of isoparametric hypersurfaces (joint work with Hui Ma), such as the formula of minimal Maslov number, complete determination of Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces and so on. More recently we obtain new results on Hamiltonian non-displaceability of the Gauss images of isoparametric hypersurfaces in another joint work with Hiroshi Iriyeh, Hui Ma and Reiko Miyaoka.

  • Research on Submanifold Theory via Infinite Dimensional Methods

    Project/Area Number : 17204006  Grant-in-Aid for Scientific Research(A) Representative

    Project Year :

    2005
    -
    2008
     

    Partaker : KATO Shin, KOMORI Yohei, SAKAI Takashi, HASHIMOTO Yoshitake

  • Differential geometry of harmonic maps, minimal submanifolds and Yang-Mills-Higgs equations

    Project/Area Number : 13440025  Grant-in-Aid for Scientific Research(B) Representative

    Project Year :

    2001
    -
    2003
     

    Partaker : MARTIN Guest, MIYAOKA Reiko, KOIKE Naoyuki, UDAGAWA Seiichi, MORIYA Katsuhiro

     View Summary

    In this project we had much research activity during the research period and we obtained the following fruitful research results. We expect fitter research progress.
    The joint work of Ohnita and Udagawa on harmonic maps of finite type was published in the proceedings of the 9-th MSJ-IRI. It is related with the equivalence problem among twisted loop algebras associated with different k-symmetric spaces and we will go to further research. And Ohnita discussed pluriharmonic maps into symmetric spaces from the viewpoint of integrable systems and proved DPW formula for pluriharmonic maps. In the joint work with James Eells on the structure of spaces of harmonic maps we started from the precise proof that the space of harmonic maps between compact real analytic Riemannian manifols is a real analytic space, and we are still working. From the viewpoint of a new area in minimal submanifold theory, Ohnita studies the Hamiltonian stability problem of Lagrangian submanifolds in K"ahler manifolds. By the Lie theoretic method, he showed that compact minimal irreducible symmetric Lagrangian submanifolds embedded in complex projective spaces are Hamiltonian stable. Moreover, we proved that compact symmetric Lagrangian submanifolds embedded in complex Euclidean spaces. And we discuss the relationship between Lagrangian submanifolds and the moment maps. Until now only known Hamiltonian stable Lagrangian submanifolds in complex projective spaces and complex Euclidean spaces. Were real projective subspaces and Clifford tori. However we gave many rich examples of Hamiltonian stable Lagrangian submanifolds in the class of Lagrangian submanifolds with parallel second fundamental form, namely symmetric Lagrangian submanifolds. Koike has succeeded in construction of theory for complex equifocal submanifolds in symmetri spaces and isoparametric submanifolds in Hilbert spaces in the case of noncompact type. It is an answer to a problem posed by Terng-Thorgergsson.

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Charge of on-campus class subject 【 display / non-display

  • Differential Geometry II

    (2018) University, Special course

  • Differential Geometry I exercise

    (2018) University, Special course

  • Differential Geometry I

    (2018) University, Special course

  • Mathematical Analysis Seminar

    (2018) Graduate school, Special course

  • Mathematical Analysis Exercise

    (2018) Graduate school, Special course

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