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International Congress on Differential Geometry in memory of Alfred Gray (1939-1998)
September 18-23, 2000
Universidad del País Vasco
Bilbao, Spain |
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Organizers
M. Fernández (chairman), R. Ibáñez, M. Macho-Stadler
View Abstracts
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The Goldberg Conjecture
by
Kouei Sekigawa
Niigata University, Japan
Oral Communication
An almost Hermitian manifold M=(M, J, g) is called an almost
Kähler manifold if the Kähler form W is closed
(or equivalently,
( S)
X, Y, Z
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g((ÑXJ)Y, Z)=0,
for all vector fields X, Y, Z on M).
A Kähler manifold (ÑJ=0) is necessarily an almost
Kähler manifold.
A non-Kähler, almost Kähler manifold is called a
strictly almost Kähler manifold.
The first example of compact strictly almost Kähler
manifold was given by W. P. Thurston ([8]), and then such
examples were given by many authors (see, for example, [1]).
An almost Kähler manifold with the integrable almost
complex structure is a Kähler manifold.
Concerning the integrability of almost Kähler manifolds,
the following conjecture posed by S. I. Goldberg is
well-known ([2]).
Date received: May 8, 2000
Copyright © 2000 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # cadq-41.
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