Curvature tensors in Kaehler manifolds

Author:
Malladi Sitaramayya

Journal:
Trans. Amer. Math. Soc. **183** (1973), 341-353

MSC:
Primary 53B35

DOI:
https://doi.org/10.1090/S0002-9947-1973-0322722-1

MathSciNet review:
0322722

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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 of curvature tensors of type *K* on *V* is isomorphic with the vector space of sym metric endomorphisms of the symmetric product of , where (Theorem 3.6). Then it is shown that admits a natural orthogonal decomposition (Theorem 5.1) and hence every is expressed as . These components are explicitly determined and then it is observed that is a certain formal tensor introduced by Bochner. We call the *Bochner-Weyl* part of *L* and the space of all these is called the *Weyl subspace* of .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1973-0322722-1

Keywords:
Hermitian and Kaehler metrics,
curvature tensor,
complex manifold,
hermitian vector space,
fundamental 2-form,
Bochner-Weyl curvature tensor,
Chern class,
Einstein manifold,
tangent bundle

Article copyright:
© Copyright 1973
American Mathematical Society