Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Kaehler Einstein structure on the cotangent bundle of a Riemannian
  manifold   We use the natural lifts of the fundamental tensor field g to the cotangent
bundle T*M of a Riemannian manifold (M,g), in order to construct an almost
Hermitian structure (G,J) of diagonal type on T*M. The obtained almost complex
structure J on T*M is integrable if and only if the base manifold has constant
sectional curvature and the second coefficient, involved in its definition is
expressed as a rational function of the first coefficient and its first order
derivative. Next one shows that the obtained almost Hermitian structure is
almost Kaehlerian. Combining the obtained results we get a family of Kaehlerian
structures on T*M, depending on one essential parameter. Next we study the
conditions under which the considered Kaehlerian structure is Einstein. In this
case (T*M,G,J) has constant holomorphic curvature.

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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin