Titlebook: Geometry of Submanifolds and Applications; Bang-Yen Chen,Majid Ali Choudhary,Mohammad Nazrul Book 2024 The Editor(s) (if applicable) and

abduction

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,Generalized Wintgen Inequalities for?,-Para Sasakian Manifold,bmanifolds where equality scenarios are valid and present several applications of the main finding. Additionally, we create an inequality for Ricci solitons to discover connections between intrinsic and extrinsic invariants.

DEI

,Gravity and?Dark Matter in?the?Framework of?Metric-Affine Geometry,erms of two independent objects: the Riemannian metric and the general affine connection. With the help of the metric tensor for contraction of Riemannain curvature of the affine connection, we formed a natural action density for gravity and matter. Using calculus of variations we derive two equatio