In this paper, we establish two sharp inequalities for the normalizedδ-Casorati curvatures of submanifolds in a Kenmotsu space form, tangent to the structure vector field of the ambient space.Moreover, we show that in both cases the equality at all points characterizes the totally geodesic submanifolds.

A statistical structure is considered as a generalization of a pair of a Riemannian metric and its Levi-Civita connection. With a pair of conjugate connections ∇ and ${\nabla }^{*}$ in the Sasakian statistical structure, we provide the normalized scalar curvature which is bounded above from Casorati curvatures on C-totally real (Legendrian and slant) submanifolds of a Sasakian statistical manifold of constant $\phi$ -sectional curvature. In addition, we give examples to show that the total space is a sphere.

In this paper, we obtain a generalized Wintgen-type inequality for submanifolds in generalized (κ,µ)-space forms. Further, we discuss the inequality for bi-slant submanifolds, semi-slant submanifolds, hemi-slant submanifolds, CR-submanifolds and slant submanifolds in various ambient spaces. In particular, we generalize some recent results of Mihai, Tohoku Math. J. 69 (2017), and Aquib et al., Tamkang J. Math. 50 (2019) and Mathematics 7(12) (2019).

Rotational surfaces in the pseudo-Galilean 3-space $G_3^1$ have some types according to pseudo-Euclidean rotations and isotropic rotations. We study rotational surfaces in $G_3^1$ with a log-linear density and investigate $\phi $-minimal rotational surfac