Classification of Casorati ideal Lagrangian submanifolds in complex space forms

Recent developments in δ-Casorati curvature invariants

“…Let M n be a Riemannian n -manifold. If there exists a point p ∈ M n such that we haveρ(p) > [δ C (n − 1)] p ,then M n does not admit any minimal Lagrangian isometric immersion into C n .For Lagrangian submanifolds in complex space forms, we also have the following results obtained by Aquib et al[3] Let M n be a Lagrangian submanifold of a complex space form M n (4c). Then we have:…”

Quantum Integral Inequalities of Simpson-Type for Strongly Preinvex Functions

“…where In the following, we show a new result analogous to the inequality (7), which can be obtained directly by taking µ = 0 in Theorem 1.…”

“…The concept of convexity has been extended in several directions, since these generalized versions have significant applications in different fields of pure and applied sciences. We only point out that convexity was recently used in differential geometry to completely classify ideal Casorati submanifolds in complex space forms (see [5][6][7][8]). One of the convincing examples on extensions of convexity is the introduction of invex function, which was introduced by Hanson [9].…”

Chen-Ricci Inequalities with a Quarter Symmetric Connection in Generalized Space Forms

“…Definition 8 (see [25]). A nontotally geodesic Lagrangian submanifold M m of a complex space form N 2m ð4cÞ is called H-umbilical if its second fundamental form satisfies…”