Abstract In this paper, we establish optimal inequalities involving generalized δ -Casorati curvature δ C ( k ; s − 1 ) for the bi-slant submanifolds of generalized Sasakian space forms endowed with a quarter-symmetric connection. The equality case is discussed for ideal submanifolds. Furthermore, the special cases of derived inequality is given for C -totally real submanifolds and some other classes of submanifolds.

中文翻译：

---

广义 Sasakian 空间形式中双斜子流形的 Chen δ 不变量型不等式

摘要 在本文中，我们为具有四分之一对称连接的广义 Sasakian 空间形式的双斜子流形建立了涉及广义 δ -Casorati 曲率 δ C ( k ; s − 1 ) 的最优不等式。讨论了理想子流形的相等情况。此外，还给出了 C -全实子流形和一些其他类子流形的导出不等式的特殊情况。