Warped Product PTR-Submanifolds in a Kähler Manifold
Makaleler > Tam Makale · 2026
Yazarlar: FIRAT YERLİKAYA, Bayram ŞAHİN
Turkish Journal of Mathematics, Uluslararası, Wos, 2026, cilt 50, ss 764-780
Özet
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.