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Associated Nijenhuis Tensors on Manifolds with Almost Hypercomplex Structures and Metrics of Hermitian–Norden Type

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Abstract

An associated Nijenhuis tensor of endomorphisms in the tangent bundle is introduced. Special attention is paid to such tensors for an almost hypercomplex structure and the metric of Hermitian–Norden type. There are studied relations between the six associated Nijenhuis tensors as well as their vanishing. It is given a geometric interpretation of the vanishing of these tensors as a necessary and sufficient condition for the existence of a unique linear connection with totally skew-symmetric torsion tensor preserving the structure. Finally, an example of a 4-dimensional manifold of the considered type with vanishing associated Nijenhuis tensors is given.

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Authors and Affiliations

  1. Department of Algebra and Geometry, Faculty of Mathematics and Informatics, Plovdiv University, 236 Bulgaria Blvd, 4027, Plovdiv, Bulgaria

    Mancho Manev

  2. Department of Medical Informatics, Biostatistics and Electronic Education, Faculty of Public Health, Medical University of Plovdiv, 15A Vasil Aprilov Blvd, 4002, Plovdiv, Bulgaria

    Mancho Manev

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  1. Mancho Manev
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Manev, M. Associated Nijenhuis Tensors on Manifolds with Almost Hypercomplex Structures and Metrics of Hermitian–Norden Type. Results Math 71, 1327–1343 (2017). https://doi.org/10.1007/s00025-016-0624-x

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  • DOI: https://doi.org/10.1007/s00025-016-0624-x

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