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For any nonnull constant<jats:italic>k<\/jats:italic>and any symmetric tensor field of type (1,\u00a01)<jats:italic>L<\/jats:italic>on<jats:italic>M<\/jats:italic>, we can define two tensor fields of type (1,\u00a02) on<jats:italic>M<\/jats:italic>,<jats:inline-formula><jats:alternatives><jats:tex-math>$$L_F^{(k)}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msubsup><mml:mi>L<\/mml:mi><mml:mi>F<\/mml:mi><mml:mrow><mml:mo>(<\/mml:mo><mml:mi>k<\/mml:mi><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:msubsup><\/mml:math><\/jats:alternatives><\/jats:inline-formula>and<jats:inline-formula><jats:alternatives><jats:tex-math>$$L_T^{(k)}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msubsup><mml:mi>L<\/mml:mi><mml:mi>T<\/mml:mi><mml:mrow><mml:mo>(<\/mml:mo><mml:mi>k<\/mml:mi><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:msubsup><\/mml:math><\/jats:alternatives><\/jats:inline-formula>, related to both connections. We study the behaviour of the structure operator<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\phi $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03d5<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>with respect to such tensor fields in the particular case of<jats:inline-formula><jats:alternatives><jats:tex-math>$$L=A$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>L<\/mml:mi><mml:mo>=<\/mml:mo><mml:mi>A<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>, the shape operator of<jats:italic>M<\/jats:italic>, and obtain some new characterizations of ruled real hypersurfaces in complex projective space.<\/jats:p>","DOI":"10.1007\/s10998-023-00532-7","type":"journal-article","created":{"date-parts":[[2023,8,10]],"date-time":"2023-08-10T13:02:01Z","timestamp":1691672521000},"page":"456-467","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["New characterizations of ruled real hypersurfaces in complex projective space"],"prefix":"10.1007","volume":"87","author":[{"given":"Juan de Dios","family":"P\u00e9rez","sequence":"first","affiliation":[]},{"given":"David","family":"P\u00e9rez-L\u00f3pez","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,8,10]]},"reference":[{"key":"532_CR1","doi-asserted-by":"crossref","unstructured":"D.E. 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