Lightlike tangent developables in de Sitter 3-space

Homology Groups in Warped Product Submanifolds in Hyperbolic Spaces

“…e geometric structure and topological properties of submanifolds in different spaces have been studied on a large scale during the past few years [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Many results showed that there is a closed relationship between stable currents which are nonexistent and the vanished homology groups of submanifolds in a different class of the ambient manifold obtained by imposing conditions on the second fundamental form (1).…”

Some Eigenvalues Estimate for the ϕ -Laplace Operator on Slant Submanifolds of Sasakian Space Forms

“…Finding the bound of the eigenvalue for the Laplacian on a given manifold is a key aspect in Riemannian geometry, and there are different classes of submanifolds such as slant submanifolds, CR-submanifolds, and singular submanifolds, which motivates further exploration and attracts many researchers from different research areas [1][2][3][4][5][6][7][8][9][10][11]. A major objective is to study the eigenvalue that appears as solutions of the Dirichlet or Neumann boundary value problems for curvature functions.…”

Null Homology Groups and Stable Currents in Warped Product Submanifolds of Euclidean Spaces

“…We proved a compact warped product submanifold M n in a Euclidean space E n+k , that there are no stable p-currents, homology groups vanish, and that M 3 is homotopic to the Euclidean sphere S 3 under various extrinsic restrictions, involving the eigenvalue of the warped function, integral Ricci curvature and the Hessian tensor. In our next work, we will combine the singularity theory presented in [31][32][33][34] to study compact warped product submanifold M n in a Euclidean space E n+k .…”