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Clifford Algebras pp 167–183Cite as

Hyper-Hermitian Manifolds and Connections with Skew-Symmetric Torsion

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Part of the book series: Progress in Mathematical Physics ((PMP,volume 34))

Abstract

The aim of the present paper is to review general results and some constructions of the hyper-Kähler geometry with torsion. This is the geometry of a special type of hyper-Hermitian metrics on a hypercomplex manifold related to some questions in theoretical physics. In particular, we show that there is a local existence of such metrics based on an HKT-potential theory, a moment map and reduction theory, as well as a global non-existence property.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Florida International University, Miami, FL, 33199, USA

    Gueo Grantcharov

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  1. Gueo Grantcharov
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Tennessee Technological University, 5054, TN 38505, Cookeville, USA

    Rafał Abłamowicz

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© 2004 Birkhäuser Boston

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Grantcharov, G. (2004). Hyper-Hermitian Manifolds and Connections with Skew-Symmetric Torsion. In: Abłamowicz, R. (eds) Clifford Algebras. Progress in Mathematical Physics, vol 34. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2044-2_11

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  • DOI: https://doi.org/10.1007/978-1-4612-2044-2_11

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-3525-1

  • Online ISBN: 978-1-4612-2044-2

  • eBook Packages: Springer Book Archive

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