Turkish Journal of Mathematics
Abstract
Recently, the PTR-submanifold of an almost Hermitian manifold has been defined and studied as a large class including CR-submanifolds, hemi-slant submanifolds, and pointwise hemi-slant submanifolds, which are well-known in the literature. This novel category of submanifolds comprises two distributions, one of which is antiinvariant while the complementary distribution is arbitrary. This paper discusses the case of a PTR-submanifold being a warped product. It is first shown that there are no such warped product submanifolds for the case where the first factor is antiinvariant. Therefore, warped product PTR-submanifolds whose second factor is antiinvariant are examined. A characterization is given for this second case, and an inequality is obtained in terms of the second fundamental form and warping function. Additionally, the situation in which the ambient space of the warped product PTR-submanifold is a complex space form is also studied in detail. In this direction, a new version of the inequality is found, and the corresponding geometric results are given accordingly.
DOI
10.55730/1300-0098.3680
Keywords
Kählermanifold, complex space form, partially totally real submanifold, warped product manifold, partially totally real warped product, CR-submanifold
First Page
764
Last Page
780
Publisher
The Scientific and Technological Research Council of Türkiye (TÜBİTAK)
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
YERLİKAYA, F, & ŞAHİN, B (2026). Warped Product PTR-Submanifolds in a Kähler Manifold. Turkish Journal of Mathematics 50 (4): 764-780. https://doi.org/10.55730/1300-0098.3680
