Let M be a Wintgen ideal submanifold of dimension n in a real space form Rn+m(k) of dimension (n + m) and of constant curvaturek, n ≥ 4, m ≥ 1. Let g, R, Ricc, g ∧ Ricc and C be the metric tensor, the Riemann-Christoffel curvature tensor, the Ricci tensor, the Kulkarni-Nomizu product of g and Ricc, and the Weyl conformal curvature tensor of M, respectively. In this paper we study Wintgen ideal submanifolds M in real space forms Rn+m(k), n ≥ 4, m ≥ 1, satisfying the following pseudo-symmetry type curvature conditions:
(i) the tensors R · C and Q(g, R) (resp., Q(g, C), Q(g, g ∧ Ricc), Q(Ricc, R) or Q(Ricc, g ∧ Ricc)) are linearly dependent;
(ii) the tensors C · R and Q(g, R) (resp., Q(g, C), Q(g, g ∧ Ricc), Q(Ricc, R) or Q(Ricc, g ∧ Ricc)) are linearly dependent;
(iii) the tensors R·C -C ·R and Q(g, R) (resp., Q(g, C), Q(g, g∧Ricc), Q(Ricc, R) or Q(Ricc, g∧Ricc)) are linearly dependent.
Tachibana tensor pseudo-symmetry type curvature condition generalized Einstein metric condition submanifold Wintgen ideal submanifold DDVV conjecture
Birincil Dil | İngilizce |
---|---|
Konular | Cebirsel ve Diferansiyel Geometri |
Bölüm | Araştırma Makalesi |
Yazarlar | |
Erken Görünüm Tarihi | 5 Nisan 2024 |
Yayımlanma Tarihi | 23 Nisan 2024 |
Gönderilme Tarihi | 13 Aralık 2023 |
Kabul Tarihi | 24 Mart 2024 |
Yayımlandığı Sayı | Yıl 2024 Cilt: 17 Sayı: 1 |