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The volumes of small geodesic balls and generalized Chern numbers of Kaehler manifolds

Published online by Cambridge University Press:  22 January 2016

Novica Blazic
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In this paper we study a connection between global and local properties of Kaehler manifolds, more specifically we study a connection between the volumes of small geodesic balls of a manifold M and some generalized Chern numbers. We use the standard power series expansion for Vm(r).

In Theorem 3.1 we give characterizations of a flat compact Kaehler manifold in terms of the volumes of small geodesic balls and generalized Chern numbers ωn-1c1(M) and ωn-2c12(M). In Theorem 4.1 similar questions for complex space forms are considered. So we prove one particular case of the Conjecture (IV) stated by Gray and Vanhecke [6].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 116 , December 1989 , pp. 181 - 189
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

References

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