We use results of Matzeu and Nikcevic to decompose the space of affine
Kaehler curvature tensors as a direct sum of irreducible modules in the complex
settin

Blažić N.

Bokan N.

García-Río E.

Higa T.

M. BROZOS-VÁZQUEZ

Matzeu P.

P. GILKEY

Phong D.

S. NIKČEVIĆ

Simon U.

Strichartz R.

English

arXiv

 In dimension m ≥ 4, results of Strichartz decompose the space 𝔄 of affine curvature tensors as a direct sum of 3 modules in the real setting and results of Bokan give a corresponding finer decomposition of 𝔄 in the Riemannian setting as the direct sum of 8 irreducible modules. In dimension m ≥ 8, results of Matzeu and Nikčević decompose the space 𝔎 of affine Kähler curvature tensors as the direct sum of 12 irreducible modules in the Hermitian setting (i.e. given an auxiliary inner product which is invariant under the given almost complex structure). In this paper, we decompose 𝔎 as a direct sum of six irreducible modules in the complex setting in dimension m ≥ 8. Corresponding decompositions into fewer modules are given in dimension m = 4 and m = 6. </jats:p

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International Journal of Geometric Methods in Modern Physics

THE STRUCTURE OF THE SPACE OF AFFINE KÄHLER CURVATURE TENSORS AS A COMPLEX MODULE

The structure of the space of affine Kaehler curvature tensors as a
  complex module

The structure of the space of affine Kaehler curvature tensors as a complex module

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