abstract: "<p>\n On an H-type manifold we describe the collection of endomorphisms of\n <inline-formula content-type=\"math/mathml\">\n \ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper H Subscript p\">\n <mml:semantics>\n \ <mml:msub>\n <mml:mrow class=\"MJX-TeXAtom-ORD\">\n \ <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">H</mml:mi>\n \ </mml:mrow>\n <mml:mi>p</mml:mi>\n \ </mml:msub>\n <mml:annotation encoding=\"application/x-tex\">\\mathcal {H}_p</mml:annotation>\n </mml:semantics>\n \ </mml:math>\n </inline-formula>\n induced by Bott-parallel transport around loops at a point\n <inline-formula content-type=\"math/mathml\">\n <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\">\n <mml:semantics>\n <mml:mi>p</mml:mi>\n \ <mml:annotation encoding=\"application/x-tex\">p</mml:annotation>\n \ </mml:semantics>\n </mml:math>\n </inline-formula>\n \ . This is a generalization of the idea of Riemannian holonomy from Riemannian geometry that respects the intrinsic structure of the horizontal bundle; the study of this horizontal holonomy is then related to the structure of the local submersions and the Riemannian holonomy of the base space.\n </p>" author: Baudoin, Fabrice and Vega-Molino, Sylvie author_list: - affiliation: [] family: Baudoin given: Fabrice - affiliation: [] family: Vega-Molino given: Sylvie citations: - article-title: A theorem on holonomy author: Ambrose, W. doi: 10.2307/1990721 first-page: '428' issn: https://id.crossref.org/issn/0002-9947 issn-type: print journal-title: Trans. Amer. Math. Soc. volume: '75' year: '1953' - article-title: Sur les groupes d’holonomie homogène des variétés à connexion affine et des variétés riemanniennes author: Berger, Marcel doi: 10.24033/bsmf.1464 first-page: '279' issn: https://id.crossref.org/issn/0037-9484 issn-type: print journal-title: Bull. Soc. Math. 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