Öz
Kaynakça
- [1] A. Bejancu, Submanifolds of a Kähler manifold I, Proc. Amer. Math. Soc. 69 (1), 135–142, 1978.
Öz
Observing the integrability of the vertical distribution in Riemannian submersions and the integrability of the anti-invariant distribution of a CR-submanifold of a K\"{a}hler manifold \cite{Chen-1981}, Kobayashi \cite{Kobayashi-1987} defined and studied CR-submersions. This notion later attracted the attention of many authors and a large number of works were published. The integrability of the anti-invariant distribution of a hemi-slant submanifold of a Kaehler manifold is also well known \cite{Sahin-2009}. In this paper, we introduce to Riemannian submersions of a hemi-slant submanifold of a K\"{a}hler manifold by using this property of hemi-slant submanifolds and the integrability of the vertical distribution of a Riemannian submersion. Using this notion, we show that the base manifold is also a K\"{a}hler manifold in the submersion of a hemi-slant submanifold of a K\"{a}hler manifold. We obtain an inequality between the sectional curvature of the hemi-slant submanifold and the holomorphic sectional curvature of the base manifold. If this inequality is equal, a geometric result is given. In addition, the Ricci tensor field on the horizontal distribution along this submersion is also found.
Anahtar Kelimeler
K\"{a}hler manifold Riemannian submersion Hemi-slant submanifold CR-submanifold Holomorphic sectional curvature
Etik Beyan
Conflict of Interests. The authors declare that they have no competing interests. Author’s contributions. All authors contributed equally to this work.
Kaynakça
- [1] A. Bejancu, Submanifolds of a Kähler manifold I, Proc. Amer. Math. Soc. 69 (1), 135–142, 1978.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Cebirsel ve Diferansiyel Geometri |
| Bölüm | Matematik |
| Yazarlar | |
| Erken Görünüm Tarihi | 11 Nisan 2025 |
| Yayımlanma Tarihi | |
| Gönderilme Tarihi | 17 Ağustos 2024 |
| Kabul Tarihi | 25 Ocak 2025 |
| Yayımlandığı Sayı | Yıl 2025 Erken Görünüm |