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This almost contact metric structure allows us to define, for any nonzero real number <jats:italic>k<\/jats:italic>, the so-called <jats:italic>k<\/jats:italic>-th generalized Tanaka\u2013Webster connection. With this connection and the Levi-Civita one we can associate two tensors of type (1,2) to the structure Jacobi operator <jats:inline-formula><jats:alternatives><jats:tex-math>$$R_{\\xi }$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>R<\/mml:mi>\n                    <mml:mi>\u03be<\/mml:mi>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> of <jats:italic>M<\/jats:italic>. We classify real hypersurfaces in complex projective space for which such tensors satisfy a cyclic property.<\/jats:p>","DOI":"10.1007\/s10998-022-00508-z","type":"journal-article","created":{"date-parts":[[2022,12,29]],"date-time":"2022-12-29T10:02:35Z","timestamp":1672308155000},"page":"110-118","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On two tensors associated to the structure Jacobi operator of a real hypersurface in complex projective space"],"prefix":"10.1007","volume":"87","author":[{"given":"Juande Dios","family":"P\u00e9rez","sequence":"first","affiliation":[]},{"given":"David","family":"P\u00e9rez-L\u00f3pez","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,12,29]]},"reference":[{"key":"508_CR1","doi-asserted-by":"publisher","first-page":"473","DOI":"10.5486\/PMD.1999.2081","volume":"54","author":"JT Cho","year":"1999","unstructured":"J.T. 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