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Curvature Tensors in Kaehler Manifolds

Malladi Sitaramayya
Transactions of the American Mathematical Society
Vol. 183 (Sep., 1973), pp. 341-353
DOI: 10.2307/1996473
Stable URL: http://www.jstor.org/stable/1996473
Page Count: 13
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Curvature Tensors in Kaehler Manifolds
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Abstract

Curvature tensors of Kaehler type (or type K) are defined on a hermitian vector space and it has been proved that the real vector space LK(V) of curvature tensors of type K on V is isomorphic with the vector space of symmetric endomorphisms of the symmetric product of V+, where $V^C = V^+ \oplus V^-$ (Theorem 3.6). Then it is shown that LK(V) admits a natural orthogonal decomposition (Theorem 5.1) and hence every L ε LK(V) is expressed as L = L1 + LW + L2. These components are explicitly determined and then it is observed that LW is a certain formal tensor introduced by Bochner. We call LW the Bochner-Weyl part of L and the space of all these LW is called the Weyl subspace of LK(V).

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