In the present paper, first we prove some results by using fundamental properties of totally real statistical submanifolds immersed into holomorphic statistical manifolds. Further, we obtain the generalized Wintgen inequality for Lagrangian statistical submanifolds of holomorphic statistical manifolds with constant holomorphic sectional curvature c. The paper finishes with some geometric consequences of obtained results.

<p class="0abstract"><strong>Abstract-</strong>The path planning for Multi Mobile Robotic (MMR) system is a recent combinatorial optimisation problem. In the last decade, many researches have been published to solve this problem. Most of these researches focused on metaheuristic algorithms. This paper reviews articles on Ant Colony Optimisation (ACO) and its hybrid versions to solve the problem. The original Dorigo’s ACO algorithm uses exploration and exploitation phases to find the shortest route in a combinatorial optimisation problem in general without touching mapping, localisation and perception. Due to the properties of MMR, adaptations have been made to ACO algorithms. In this review paper, a literature survey of the recent studies on upgrading, modifications and applications of the ACO algorithms has been discussed to evaluate the application of the different versions of ACO in the MMR domain. The evaluation considered the quality, speed of convergence, robustness, scalability, flexibility of MMR and obstacle avoidance, static and dynamic environment characteristics of the tasks. <strong></strong></p>

In this paper, we prove sharp inequalities between the normalized scalar curvature and the generalized normalized δ-Casorati curvatures for different submanifolds in Bochner Kaehler manifold. Moreover, We also characterize submanifolds on which the equalities hold.

B. Y. Chen established sharp inequalities between certain Riemannian invariants and the squared mean curvature for submanifolds in real space form as well as in complex space form. In this paper we generalize Chen inequalities for submanifolds of Bochner Kaehler manifolds. Moreover, we consider CR-warped product submanifolds of Bochner Kaehler manifold and establish an inequality for scalar curvature.