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Angles in normed spaces

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Abstract

The concepts of angle, angle functions, and the question how to measure angles present old and well-established mathematical topics referring to the Euclidean space, and there exist also various extensions to non-Euclidean spaces of different types. In particular, it is very interesting to investigate or to combine (geometric) properties of possible concepts of angle functions and angle measures in finite-dimensional real Banach spaces (= Minkowski spaces). However, going into this direction one will observe that there is no monograph or survey reflecting the complete picture of the existing literature on such concepts in a satisfying manner. We try to close this gap. In this expository paper (containing also new results, and new proofs of known results) the reader will get a comprehensive overview of this field, including further related aspects, as well. For example, angular bisectors, their applications, and angle types which preserve certain kinds of orthogonality are discussed. The latter aspect yields, of course, an interesting link to the large variety of orthogonality types in such spaces.

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Authors and Affiliations

  1. CEFET/RJ Campus Nova Friburgo, Nova Friburgo, 28635-000, Brazil

    Vitor Balestro

  2. Instituto de Matemática e Estatística, Universidade Federal Fluminense, Niterói, 24020-140, Brazil

    Vitor Balestro & Ralph Teixeira

  3. Institute of Mathematics, Budapest University of Technology and Economics, 1111, Budapest, Hungary

    Ákos G. Horváth

  4. Department of Applied Mathematics, Harbin University of Science and Technology, Harbin, 150080, China

    Horst Martini

  5. Fakultät für Mathematik, Technische Universität Chemnitz, 09107, Chemnitz, Germany

    Horst Martini

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  1. Vitor Balestro
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  2. Ákos G. Horváth
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  3. Horst Martini
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  4. Ralph Teixeira
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Correspondence to Vitor Balestro.

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V. Balestro thanked CAPES for partial financial support during the preparation of this manuscript.

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Balestro, V., Horváth, Á.G., Martini, H. et al. Angles in normed spaces. Aequat. Math. 91, 201–236 (2017). https://doi.org/10.1007/s00010-016-0445-8

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