SAKANE Yusuke

J-GLOBAL         Last updated: Nov 12, 2019 at 14:29
 
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Name
SAKANE Yusuke
URL
http://www4.math.sci.osaka-u.ac.jp/~sakane/
Affiliation
Osaka University
Job title
Professor Emeritus
Degree
Ph.D.(Dept. of Math. University of Notre Dame)

Research Interests

 
 

Research Areas

 
 

Education

 
 
 - 
1974
Mathematics, Graduate School, Division of Mathematics, University of Notre Dame
 
 
 - 
1968
Faculty of Science, Osaka University
 

Published Papers

 
A. Arvanitoyeorgos , Y. Sakane and M. Statha
Recent Topics in Differential Geometry and its Related Fields, Proceedings of the 6th International Colloquium on Differential Geometry and its Related Fields,   5-27   Oct 2019   [Refereed]
A. Arvanitoyeorgos, Y. Sakane and M. Statha
Advances in Geometry   18(4) 509-524   Oct 2018   [Refereed]
A. Arvanitoyeorgos, Y. Sakane and M. Statha
Contemporary Perspectives in Differential Geometry and its Related Fields, Proceedings of the 5th International Colloquium on Differential Geometry and its Related Fields,   1-20   Nov 2017   [Refereed]
Ioannis Chrysikos, Yusuke Sakane
Journal of Geometry and Physics   116 152-186   Jun 2017   [Refereed]
A. Arvanitoyeorgos , Y. Sakane and M. Statha
Current Developments in Differential Geometry and its Related Fields, Proceedings of the 4th International Colloquium on Differential Geometry and its Related Fields,   1-22   Dec 2015   [Refereed]
A. Arvanitoyeorgos , Y. Sakane and M. Statha
Geometry, Imaging and Computing   2(2) 77-108   Dec 2015   [Refereed]
A. Arvanitoyeorgos, Y. Sakane and M. Statha
Differential Geom. Appl.   35(Supplement) 2-18   Sep 2014   [Refereed]
Ioannis Chrysikos, Yusuke Sakane
Bulletin des Sciences Mathématiques   138(6) 665-692   Sep 2014   [Refereed]
Let Tex be a simple compact connected Lie group. We study homogeneous
Einstein metrics for a class of compact homogeneous spaces, namely generalized
flag manifolds Tex with second Betti number Tex. There are 8
infinite families Tex ...
A. Arvanitoyeorgos, I. Chrysikos and Y. Sakane
Prospects of Differential Geometry and its Related Fields   15-38   Nov 2013   [Refereed]
Andreas Arvanitoyeorgos, Ioannis Chrysikos, Yusuke Sakane
International Journal of Mathematics   24(10) 1-52   Sep 2013   [Refereed]
We construct the homogeneous Einstein equation for generalized flag manifolds Tex of a compact simple Lie group Tex whose isotropy representation decomposes into five inequivalent irreducible Tex-submodules. To this end we apply a new tech...
Rachid Ait-Haddou, Yusuke Sakane, Taishin Nomura
Journal of Computational and Applied Mathematics   247(1) 172-208   Aug 2013   [Refereed]
The notion of blossom in extended Chebyshev spaces offers adequate
generalizations and extra-utilities to the tools for free-form design schemes.
Unfortunately, such advantages are often overshadowed by the complexity of the
resulting algorithms. ...
A. Arvanitoyeorgos, I. Chrysikos and Y. Sakane
J. Symbolic Comput.   55 59-71   Aug 2013   [Refereed]
Andreas Arvanitoyeorgos, Ioannis Chrysikos, Yusuke Sakane
Proc. Amer. Math. Soc.   141(7) 2485-2499   Mar 2013   [Refereed]
We construct the Einstein equation for an invariant Riemannian metric on the
exceptional full flag manifold Tex. By computing a Gröbner basis for a
system of polynomials of multi-variables we prove that this manifold admits
exactly two non...
Rachid Ait-Haddou, Yusuke Sakane, Taishin Nomura
Computer Aided Geometric Design   30(2) 240-253   Feb 2013   [Refereed]
By identifying a family of corner cutting schemes as a dimension elevation
process of Gelfond-Bezier curves, we give a Muntz type condition for the
convergence of the generated control polygons to the underlying curve. The
surprising emergence of ...
Rachid Ait-Haddou, Yusuke Sakane, Taishin Nomura
Computer Aided Geometric Design   30(2) 199-225   Feb 2013   [Refereed]
We show that the generalized Bernstein bases in Muntz spaces defined by
Hirschman and Widder [7] and extended by Gelfond [6] can be obtained as limits
of the Chebyshev-Bernstein bases in Muntz spaces with respect to an interval
[a,1] as the real n...
Andreas Arvanitoyeorgos, Kunihiko Mori, Yusuke Sakane
Geom. Dedicata   160(1) 261-285   Oct 2012   [Refereed]
The study of left-invariant Einstein metrics on compact Lie groups which are
naturally reductive was initiated by J. E. D'Atri and W. Ziller in 1979. In
1996 the second author obtained non-naturally reductive Einstein metrics on the
Lie group SU(n...
Andreas Arvanitoyeorgos, Ioannis Chrysikos, Yusuke Sakane
Recent Progress in Differential Geometry and Its Related Fields   1-24   Sep 2011   [Refereed]
We find the precise number of non-Kähler Tex-invariant Einstein metrics
on the generalized flag manifold Tex with Tex
and Tex. We use an analysis on parametric systems of polynomial
equations and...
A. Arvanitoyeorgos, I. Chrysikos and Y. Sakane
Differential Geom. Appl.   29(suppl. 1) S16-S27   Aug 2011   [Refereed]
Andreas Arvanitoyeorgos, Ioannis Chrysikos, Yusuke Sakane
Annals of Global Analysis and Geometry   38(4) 413-438   Dec 2010   [Refereed]
We find the precise number of non-Kähler Tex-invariant Einstein
metrics on the generalized flag manifold Tex with
Tex and Tex. We use an analysis on parametric systems of
polynomial equations and...

Misc

 
Bezier curves and Bezier surfaces
sugaku 56   56巻 2号    2004
Harmonic forms on compact symplectic 2-step nilmanifolds
Y. Sakane and T. Yamada
Geometry, Integrability and Quantization IV   257-270   2003   [Refereed]
Harmonic cohomology groups of compact symplectic nilmanifolds
Y. Sakane and T. Yamada
Contemp. Math.   308 287-296   2002   [Refereed]
Homogeneous Einstein metrics on flag manifolds
Y. Sakane
Lobachevskii J. Math.   4 71-87   1999   [Refereed]
J.-S. Park and Y. Sakane
Tokyo J. Math.   20(1) 51-61   1997   [Refereed]
Invariant Einstein metrics on Certain homogeneous spaces
Tokyo J. Math., 20   20    1997
Non-homogeneous Kahler-Einstein metrics on compact complex manifolds (with N. Koiso)
Osaka J. Math   25 933-959   1988
Non-homogeneous Kahler-Einstein metrics on compact complex manifolds
Osaka J. Math., 25   25    1988
Non-homogeneous Kahler-Einstein metrics on compact complex manifolds II
N. KOISO AND Y. SAKANE
Osaka J. Math.   25(4) 933-959   1988   [Refereed]
Non-homogeneous Kahler-Einstein metrics on compact complex manifolds
Lecture Notes in Math., 1201   1201    1986

Books etc

 
Non-homogeneous Kahler-Einstein metrics on compact complex manifolds( with N. Koiso)
Curvature and Topology of Riemannian manifolds, Lecture Note in Math. , Springer-Verlag   1986   
Homogeneous Einstein metrics on a principal circle bundles
Complex Geometry, Lecture Notes in Pure and Appl. Math. , Marcel Dekker   1993   
Introduction to Modern Mathematics, III
Osaka University Press   2002   
Complex Geometry
Lecture Notes in Pure and Applied Mathematics, 143, Marcel Dekker   1993   

Research Grants & Projects

 
Study on Einstein manifolds
Fundamentals of CAGD