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On the Non-triviality of the Eight-Form \(\tau _4(\omega )\) on Manifolds with a \(\mathrm {Spin}(9)\)-Structure

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Geometry, Algebra and Applications: From Mechanics to Cryptography

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 161))

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Abstract

It is proved that Parton-Piccinni’s expression \(\tau _4(\omega )\) of the canonical 8-form on a manifold with holonomy group \(\mathrm {Spin}(9)\) is not trivial, by using the properties of the octonions.

Dedicated to Jaime Muñoz Masqué on the occasion of his 65th birthday.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Cracow University of Technology, Warszawska 24, 31155, Cracow, Poland

    I. V. Mykytyuk

  2. Institute of Applied Problems of Mathematics and Mechanics, Naukova Str. 3b, Lviv, 79601, Ukraine

    I. V. Mykytyuk

Authors
  1. I. V. Mykytyuk
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Correspondence to I. V. Mykytyuk .

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Editors and Affiliations

  1. Departamento de Geometría y Topología, Universidad Complutense de Madrid, Madrid, Spain

    Marco Castrillón López

  2. Physical and Information Technology, Spanish National Research Council (CSIC), Madrid, Spain

    Luis Hernández Encinas

  3. Institute of Fundamental Physics, Spanish National Research Council (CSIC), Madrid, Spain

    Pedro Martínez Gadea

  4. Departamento de Matemática Aplicada, Universidad Politécnica de Madrid, Madrid, Spain

    Mª Eugenia Rosado María

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Mykytyuk, I.V. (2016). On the Non-triviality of the Eight-Form \(\tau _4(\omega )\) on Manifolds with a \(\mathrm {Spin}(9)\)-Structure. In: Castrillón López, M., Hernández Encinas, L., Martínez Gadea, P., Rosado María, M. (eds) Geometry, Algebra and Applications: From Mechanics to Cryptography. Springer Proceedings in Mathematics & Statistics, vol 161. Springer, Cham. https://doi.org/10.1007/978-3-319-32085-4_15

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