NAITOH Hiroo

J-GLOBAL         Last updated: Mar 26, 2016 at 02:45
 
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Name
NAITOH Hiroo
E-mail
naitohyamaguchi-u.ac.jp
URL
http://www.sci.yamaguchi-u.ac.jp/ms/index.html
Affiliation
Yamaguchi University
Section
Graduate School of Science and Engineering Natural Sciences and Mathematics(Science) Graduate School of Science and Engineering(Science) YAMAGUCHI UNIVERSITY
Job title
Professor
Degree
Doctor of Science(Osaka University), Master of Science(Osaka University), Bachelor of Science(Osaka University)
Research funding number
10127772

Research Areas

 
 

Academic & Professional Experience

 
Apr 1997
 - 
Today
Professor, Graduate School of Science and Engineering(Science), YAMAGUCHI UNIVERSITY
 
May 2009
 - 
Mar 2010
YAMAGUCHI UNIVERSITY
 
Apr 2010
 - 
Today
Vice-President, YAMAGUCHI UNIVERSITY
 

Education

 
 
 - 
Mar 1975
mathematics, Faculty of Science, Osaka University
 
 
 - 
Sep 1979
Mathematics, Graduate School, Division of Natural Science, Osaka University
 

Published Papers

 
On cut loci and first conjugate loci of the irreducible symmetric R-spaces
Hiroo Naitoh
Hokkaido Mathematical Journal   6(2) 231-242   1977   [Refereed]
Isotropic submanifolds with parallel second fundamental forms in symmetric spaces
Hiroo Naitoh
Osaka Journal of Mathematics   17(1) 95-110   1980   [Refereed]
Isotropic submanifolds with parallel second fundamental form in Pm(C)
Hiroo Naitoh
Osaka Journal of Mathematics   18(2) 427-464   1981   [Refereed]
Totally real parallel submanifolds in Pn(C)
Hiroo Naitoh
Tokyo Journal of Mathematics   4(2) 279-306   1981   [Refereed]
On conjugate points of a nilpotent Lie group
[Hiroo Naitoh][Yusuke Sakane]
Tsukuba Journal of Mathematics   5(1) 143-152   1981   [Refereed]

Misc

 
Symmetry and symmetric space
Hiroo Naitoh
Sugaku Seminar   31(12) 40-45   Nov 1992

Conference Activities & Talks

 
Real hypersurfaces with Φ-invariant shape operator of complex projective spaces
[Sadahiro Maeda][Hiroo Naitoh]
Anual Meetings of the Mathematical Society of Japan (Section of Geometry)   24 Mar 2010   
Submanifolds of symmetric spaces and their Grassmann geometry
Hiroo Naitoh
Autumn Meetings of the Mathematical Society of Japan (Section of Geometry)   27 Sep 1994   
Computational approach to the classification problem of totally geodesic submanifolds of symmetric spaces
Hiroo Naitoh
Meetings: Theory of Submanifolds, Yuzawa 2009   26 Nov 2009   
Grassmann geometry on unimodular Lie groups
Hiroo Naitoh
Meetings: Lie groups and Geometric structures, Hiroshima   8 Oct 2008   
Grassmann geometry on 3-dimensional unimodular Lie groups
Hiroo Naitoh
Meetings: Geometric structures on manifolds and its application, Nagoya   6 Mar 2008   

Teaching Experience

 

Research Grants & Projects

 
Study on the theory of submanifolds of compact Riemannian symmetric spaces
Project Year: Apr 1997 - Mar 1999
Study on the theory of submanifolds of compact Riemannian symmetric spaces
Project Year: Apr 1997 - Mar 1999
Study on totally geodesic submanifolds of symmetric spaces
Project Year: Apr 2001 - Mar 2005
Study on totally geodesic submanifolds of symmetric spaces
Project Year: Apr 2001 - Mar 2005
Study on totally geodesic submanifolds of symmetric spaces
Project Year: Apr 2001 - Mar 2005

Others

 
2001
This investigation is on totally geodesic submanifolds of Riemannian symmetric spaces and the Grassmann geometry of submanifolds associated with them. Such typical submanifolds are symmetric submanifolds.
1.Fundamental results on symmetric submanifolds
(1)We clarified the relationship between the construction of symmetric submanifolds and
the theory of Jordan triple system and the associated symmetric R-space, and obtained a summary on the history and transition on these research fields.
(2)We next clarified the details of symmetric submanifolds in the higher-rank irreducible
Riemannian symmetric spaces of noncompact type. This is a collaboration with Berndt, Eschenburg, and Tsukada.
(3)Summing up these results, we published a paper on the classification of symmetric
submanifolds of general Riemannian symmetric spaces in Japanese. This is a collaboration
with Tsukada. This result was announced in a JSPS-DFG seminar held at Kyoto University. A translation of this paper will be also issued in the journal 'Sugaku Expositions' of the American Mathematical Society.
2. Development into another Grassmann geometry
As a development of this research, we also studied the Grassm
2005
This study is on the Grassmann geometry on the Riemannian homogeneous spaces. Our aim is to consider the classification problem of extrinsic homogeneous submanifolds of Riemannian symmetric spaces. For this, in this study, we examine the case where a Riemannian homogeneous space is a 3-dimensional unimodular Lie group with a left invariant metric. The 3-dimensional unimodular Lie groups are classified into six ones; the 3-dimensional vector group, the 3-dimensional Heisenberg group, the groups of rigid motions of the Eucliden 2-plane and the Minkowski 2-plane, the special unitary group SU(2), and the special linear group SL(2,R). Also, for each of them the geometric properties such as the curvatures, the isometry group, and so on, can be expressed concretely. In this study we in particular consider the Grassmann geometry on the spaces SU(2) and SL(2,R), while the cases of the Heisenberg group and the groups of rigid motions of the Eucliden 2-plane and the Minkowski 2-plane are clarify by H. Naitoh, J. Inoguchi, and K. Kuwabara.
The obtained main results are the following.:
for both the spaces SU(2) and SL(2,R),
(1) the classification for all the orbits associated with Gras