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Volume-preserving geodesic symmetries on four-dimensional Hermitian Einstein spaces

Published online by Cambridge University Press:  22 January 2016

J. T. Cho ,
K. Sekigawa  and
L. Vanhecke
J. T. Cho
Affiliation:
Topology and Geometry, Research Center, Kyungpook National University, Taegu 702-701, Korea
K. Sekigawa
Affiliation:
Department of Mathematics, Niigata University, Niigata 950-21, Japan
L. Vanhecke
Affiliation:
Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
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Abstract.

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We prove that a four-dimensional Hermitian Einstein space is weakly *-Einsteinian and use this result to show that all geodesic symmetries are volume-preserving (up to sign) if and only if it is local symmetric.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 146 , June 1997 , pp. 13 - 29
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1997

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