Collected Papers of Yozo Matsushima

779 Pages·1992·117.53 MB·English

by  Yozo Matsushima

Collected Papers of
Yoz6 Matsushima
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COLLECTED PAPERS OF YOZO MATSUSHIMA
Copyright © 1992 by World Scientific Publishing Co. Pie. Lid.
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Series in Pure Mathematics - Volume 15
Collected Papers of
Yozo Matsushima
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V
Yozo MATSUSHIMA
1921-1983
On April 9, 1983, Yozo Matsushima, professor of Osaka University, suc
cumbed to pneumonia in Osaka at the age of 62 years. His premature death
produced no small effect among his colleagues and friends, and thus we would
like to recall here the history of his life as it relates to the mathematical com
munity.
Born on February 11, 1921 in Sakai City, Osaka Prefecture, he received
his early education at the former Naniwa High School. In September 1942, he
received his Bachelor of Science in mathematics from Osaka Imperial Univer
sity and immediately became an assistant in the Faculty of Science at the then
newly established Nagoya Imperial University. Thus began Ills career as a
mathematician.
Within a short time, he was promoted to associate professor and in 1953
to full professor at Nagoya University. In the spring of 1960, he became a
professor of Osaka University as successor to the chair of the late Kenjiro Shoda,
who had been his former teacher and was at that time president of Osaka Uni
versity. During his professorship there, he was instrumental in organizing the
mathematics department. Also at his suggestion and through his help, the
Osaka Mathematical Journal and the Journal of Mathematics, Osaka City Uni
versity, were combined within a single publication, the Osaka Journal of Math
ematics.
In September of 1966, he became professor at the University of Notre
Dame, in Notre Dame, Indiana in the U.S. and remained so for fourteen years.
In the summer of 1980, he returned to the Faculty of Science at Osaka Uni
versity.
Before going to Notre Dame, Matsushima had been recognized not only
in Japan, but also abroad, as is evidenced in the following events. In Sep
tember of 1954, he spent one year in France, at the Universities of Strasbourg
and of Paris, where he had been invited by C.N.R.S. From September of
1962, he studied for one year at the Institute for Advanced Study in Princeton,
New Jersey. In the fall of 1965 he returned to France where he was visiting
professor at the University of Grenoble for one year. In the summer of 1965,
he organized the U.S.-Japan Seminar on Differential Geometry together with
Kentaro Yano and Katsumi Nomizu at the Research Institute for Mathematical
Sciences at Kyoto University. This was the first international congress in
Japan for geometers, and eleven mathematicians from the United States par
ticipated.
Reprinted from Osaka J. Math. <1) 21 (1984).
vi
In 1962, Matsushima received the coveted Asahi Prize for his "Research
of Continuous Groups". In 1967 he became a member of the first editorial
board of the then newly established Journal of Differential Geometry and re
mained one of its editors throughout his lifetime. In May of 1980, prior to
Matsushima's return to Osaka University, some fifty of his colleagues, former
and present, showed their appreciation and respect for him by their participation
in a conference in geometry held in his honor at the University of Notre Dame.
In honor of his sixtieth birthday in February of 1981, a volume of papers was
dedicated to Matsushima. Besides those papers written by his former students
and colleagues especially for this occasion, some of the works presented at the
above mentioned conference were also included in the volume which is entitled
"Manifolds and Lie Groups, Papers in Honor of Yozo Matsushima", edited by
J. Hano et al. and published by Birkhauser.
As is outlined comprehensively in the following article generously con
tributed by Professor Shoshichi Kobayashi, in Matsushima's many mathematical
works the emphasis is on the theory of Lie groups and manifolds. His works on
these theories and on related topics such as discrete groups, unitary representa
tions, and functions of several complex variables have already proven to be
valuable references in many current papers.
Matsushima's love for mathematics is evidenced by the discipline and
diligence he consistently applied to his research. He was a man whose con
cern lay not only in mathematics, but he had a keen interest in human nature
and a constant curiosity about the world that resulted in his being an avid reader
of a variety of books and a most interesting conversationalist. His friends and
colleagues will miss not only his mathematical talent, but the warmth and cy
nical humour which lay behind his outwardly serious countenance.
Shingo MURAKAMI
vii
Contents
Yozo Mateushima (1921-1983) v
S. Murakami
The mathematical work of Y. Matsushima and its development 1
S. Kobayashi
Bemerkungen iiber die Liesche Ringe mit Primzahlcharakteristik 18
Uber die multiplikative Gruppen einer p-adischen Divisionalgebra 21
(with T. Nakayama)
Note on the replicas of matrices 28
On the Cartan decomposition of a Lie algebra 36
On algebraic Lie groups and algebras 39
On the faithful representations of Lie groups 51
On the decomposition of an (L)-group 59
On a type of subgroups of a compact Lie group 70
On the discrete subgroups and homogeneous spaces of nilpotent Lie groups 85
Some remarks on the exceptional simple Lie group S4 101
On a theorem concerning the prolongation of a differential system 107
Sur le prolongement d'un pseudogroupe d'isomorphismes
locaux d'une variete differentiable 123
Sur les algebres de Lie lineaire semi-involutives 131
Pseudo-group es de Lie transitifs 148
Un theoreme sur les espaces homogenes complexes 162
Sur les espaces homogenes kahleriens d'un groupe de Lie reductif 164
Some studies on Kaehlerian homogeneous spaces 172
(with Hand)
Sur la structure du groupe d'homeomorphismes analytiques
d'une certaine variete kaehlerinne 188
Fibres holomorphes sur un tore complexe 194
viii
Sur certains espaces fibres holomorphes sur une variete de Stein 218
(with A. Morimoto)
Espaces homogenes de Stein des groupes de Lie complexes 237
Sur certaines varietes homogenes complexes 251
Espaces homogenes de Stein des groupes de Lie complexes, H 263
On the first Betti number of compact quotient spaces of
higher-dimensional symmetric spaces 275
On Betti numbers of compact, locally symmetric Riemannian manifolds 294
On vector bundle valued harmonic forms and automorphic
forms on symmetric Riemannian manifolds 314
(with S. Murakami)
On the cohomology groups attached to certain vector valued
differential forms on the product of the upper half-planes 366
(with G. Shimura)
On the cohomology groups of locally symmetric, compact
Riemannian manifolds 399
On certain cohomology groups attached to Hermitian symmetric spaces 405
(with S- Murakami)
On certain cohomology groups attached to Hermitian symmetric spaces 440
(with S. Murakami)
A formula for the Betti numbers of compact locally symmetric
Riemannian manifolds 453
Affine structures on complex manifolds 464
On certain cohomology groups attached to Hermitian symmetric spaces (II) 472
Holomorphic vector fields and the first Chern class of a Hodge manifold 491
On the automorphisms and equivalences of generalized Siegel domains 495
(with W. Kaup and T. Ochiai)
On automorphisms and equivalences of Siegel domains 519
Vector bundle valued harmonic forms and immersions of Riemannian
manifolds 428
On Hodge manifolds with zero first Chern class 441
On the tube domains 448
Remarks on KahleT-Einstein manifolds 464
Ample vector bundles on compact complex spaces 477
(with W. Stoll)
ix
Holomorphic immersions of a compact Kahler manifold into complex tori 514
Weakly ample vector bundles and submanifolds of complex tori 534
(with A. Howard)
On a problem of Stoll concerning a cohomology map from a flag manifold
into a Grassmann manifold 574
Heisenberg groups and holomorphic vector bundles over a complex torus 613
On the intermediate cohomology group of a holomorphic line
bundle over a complex torus 648
List of publications 663
List of Ph.D. theses written under the supervision of Yozo Matsushima 667