In this paper, we study the curvature of a semi-Riemannian manifold M̃ of quasi-constant curvature admits some half lightlike submanifolds M . The main result is two characterization theorems for M̃ admits extended screen homothetic and statical half lightlike submanifolds M such that the curvature vector field of M̃ is tangent to M .

Dirac submanifolds are a natural generalization in the Poisson category for symplectic submanifolds of a symplectic manifold. In a certain sense they correspond to symplectic subgroupoids of the symplectic groupoid of the given Poisson manifold. In particular, Dirac submanifolds arise as the stable locus of a Poisson involution. In this paper, we provide a general study for these submanifolds i...

Pseudo-parallel (shortly PP) submanifolds are defined as a generalization of semi-parallel (shortly SP ) submanifolds and as extrinsic analogue of pseudo-symmetric (shortly PS) manifolds (in the sense of R. Deszcz) [1], [26]. Asperti et al [1] obtained a description of PP hypersurfaces in space form as quasiumbilic hypersurfaces or cyclids of Dupin and studied PP surfaces with maximal first nor...

In this paper, we introduce some inequalities for screen homothetic half lightlike submanifolds of a real space form constant sectional curvature , endowed with semi-symmetric metric connection. Using these inequalities, derive characterizations such submanifolds. Finally, Chen-Ricci are calculated. Morever, the equality cases considered and get results.

The aim of the present paper is to study Chen inequalities for slant, bi-slant and semi-slant submanifolds in generalized complex space forms.

Let Mn+p p (c) be n + p-dimensional connected semi-Riemannian manifold of constant curvature c whose index is p. It is called indefinite space form of index p. Let M be an n-dimensional Riemannian manifold immersed in Mn+p p (c). The semi-Riemannian metric of Mn+p p (c) induces the Riemannian metric of M , M is called a spacelike submanifold. Spacelike submanifolds in indefinite space form Mn+p...

The simplest patterns of qualitative changes on the configurations of lines of principal curvature around umbilic points on surfaces whose immersions into R3 depend smoothly on a real parameter (codimension one umbilic bifurcations) are described in this paper. Global effects, due to umbilic bifurcations, on these configurations such as the appearance and annihilation of periodic principal line...

Our paper explores warped product pointwise semi-slant submanifolds with a semi-symmetric metric connection in an odd-dimensional sphere and uncovers fundamental results. We also demonstrate how our findings can be applied to the homology of these submanifolds. Notably, we prove that under specific condition, there are no stable currents for This work adds valuable insights into stability behav...