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Preliminaries

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Book cover Nearly Pseudo-Kähler Manifolds and Related Special Holonomies

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2201))

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Abstract

In this section we collect some basic facts about stable forms, their orbits and their stabilisers.

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Notes

  1. 1.

    Here G 0 is the identity component of a Lie group G. 

  2. 2.

    Please note that in our convention 2p refers to the negative directions.

  3. 3.

    As above 0 denotes the annihilator.

  4. 4.

    See for example [100, pp. 209–211] for the curvature of warped products.

  5. 5.

    In our convention m + 1 is the number of negative directions.

  6. 6.

    Note, that the frame bundle of a para-Kähler manifold can be reduced to the bundle of para-unitary frames \(P_{U(P_{0},g_{0})}\).

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  1. Institut Differentialgeometrie, Leibniz Universität Hannover, Hannover, Germany

    Lars Schäfer

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Schäfer, L. (2017). Preliminaries. In: Nearly Pseudo-Kähler Manifolds and Related Special Holonomies. Lecture Notes in Mathematics, vol 2201. Springer, Cham. https://doi.org/10.1007/978-3-319-65807-0_2

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