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

Keywords: Pointwise semi-slant submersion, pointwise semi-slant submanifold, pointwise semi-slant Riemannian map, Kaehler manifold, Riemannian map

Abstract

UDC 514

As a natural generalization of slant submanifolds [B.-Y. Chen, Bull. Austral. Math. Soc., 41, No. 1, 135 (1990)], slant submersions [B. Şahin, Bull. Math. Soc. Sci. Math. Roumanie (N.S.), 54, No. 102, 93 (2011)], slant Riemannian maps [B. Şahin, Quaestion. Math., 36, No. 3, 449 (2013) and Int. J. Geom. Methods Mod. Phys., 10, Article 1250080 (2013)], pointwise slant submanifolds [B.-Y. Chen, O. J. Garay, Turk. J. Math., 36, 630 (2012)], pointwise slant submersions [J. W. Lee, B. Şahin, Bull. Korean Math. Soc., 51, No. 4, 1115 (2014)], pointwise slant Riemannian maps [Y. Gündüzalp, M. A. Akyol, J. Geom. and Phys., 179, Article 104589 (2022)], semi-slant submanifolds [N. Papaghiuc, Ann. Ştiinƫ. Univ. Al. I. Cuza Iaṣi. Mat. (N.S.), 40, 55 (1994)], semi-slant submersions [K.-S. Park, R. Prasad, Bull. Korean Math. Soc., 50, No. 3, Article 951962 (2013)], and semi-slant Riemannian maps [K.-S. Park, B. Şahin, Czechoslovak Math. J., 64, No. 4, 1045 (2014)], we introduce a new class of Riemannian maps, which are called {\it pointwise semi-slant Riemannian maps,} from Riemannian manifolds to almost Hermitian manifolds. We first give some examples, present a characterization, and obtain the geometry of foliations in terms of the distributions involved in the definition of these maps. We also establish necessary and sufficient conditions for pointwise semi-slant Riemannian maps to be totally geodesic and harmonic, respectively. Finally, we determine the Casorati curvatures for pointwise semi-slant Riemannian maps in the complex space form.

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