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Curvature Tensors in Kaehler Manifolds
Transactions of the American Mathematical Society
Vol. 183 (Sep., 1973), pp. 341-353
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/1996473
Page Count: 13
You can always find the topics here!Topics: Tensors, Curvature, Vector spaces, Inner products, Mathematical manifolds, Linear transformations, Mathematical theorems, Tangents, Coordinate systems, Isomorphism
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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).
Transactions of the American Mathematical Society © 1973 American Mathematical Society