Pointwise semi-slant Riemannian maps into almost Hermitian manifolds and Casorati inequalities

M. A.  Akyol; Y.  Gündüzalp

doi:10.3842/umzh.v76i9.7652

M. A. Akyol Department of Mathematics, Faculty of Arts and Sciences, Bingöl University, Turkey
Y. Gündüzalp Department of Mathematics, Faculty of Science, Dicle University, Diyarbakir, Turkey

DOI: https://doi.org/10.3842/umzh.v76i9.7652

Анотація

УДК 514

Точкові напівпохилі ріманові відображення на майже ермітових многовидах і нерівності Казораті

Як природне узагальнення похилих підмноговидів [B.-Y. Chen, Bull. Austral. Math. Soc., 41, No. 1, 135 (1990)], похилих занурень [B. Şahin, Bull. Math. Soc. Sci. Math. Roumanie (N.S.), 54, No. 102, 93 (2011)], похилих ріманових відображень [B. Şahin, Quaestion. Math., 36, No. 3, 449 (2013) та Int. J. Geom. Methods Mod. Phys., 10, Article 1250080 (2013)], точково похилих підмноговидів [B.-Y. Chen, O. J. Garay, Turk. J. Math., 36, 630 (2012)], точково похилих занурень [J. W. Lee, B. Şahin, Bull. Korean Math. Soc., 51, No. 4, 1115 (2014)], точково похилих ріманових відображень [Y. Gündüzalp, M. A. Akyol, J. Geom. and Phys., 179, Article 104589 (2022)], напівпохилих підмноговидів [N. Papaghiuc, Ann. Ştiinƫ. Univ. Al. I. Cuza Iaṣi. Mat. (N.S.), 40, 55 (1994)], напівпохилих занурень [K.-S. Park, R. Prasad, Bull. Korean Math. Soc., 50, No. 3, Article 951962 (2013)], та напівпохилих ріманових відображень [K.-S. Park, B. Şahin, Czechoslovak Math. J., 64, No. 4, 1045 (2014)], введено новий клас ріманових відображень, які названо {\it точковими напівпохилими рімановими відображеннями} від ріманових многовидів до майже ермітових многовидів. Спочатку наведено кілька прикладів, дано характеристику та отримано геометрію розшарувань в термінах розподілів, що беруть участь у визначенні таких відображень. Також визначено необхідні та достатні умови для того, щоб точкові напівпохилі ріманові відображення були повністю геодезичними та гармонічними відповідно. Крім того, отримано кривини Касораті для точкових напівпохилих ріманових відображень у комплексній просторовій формі.

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