This article covers the geometric study of pointwise slant and semi-slant submanifolds a para-Cosymplectic manifold M? 2m+1 with semi-Riemannian metric. We give an advanced definition these type for spacelike timelike vector fields. obtain characterization results involutive totally geodesic foliation such 2m+1.

It was recently shown by R. Souam and E. Toubiana [33] that the (non constantly curved) Berger spheres do not contain totally umbilic surfaces. Nevertheless in this article we show, by perturbative arguments, that all analytic metrics su ciently close to the round metric g0 on S possess generalized totally umbilic 2-spheres, namely critical points of the conformal Willmore functional ∫ Σ |A◦|2 ...

Abstract. We use a new variational method—based on the theory of anti-selfdual Lagrangians developed in [2] and [3]—to establish the existence of solutions of convex Hamiltonian systems that connect two given Lagrangian submanifolds in R . We also consider the case where the Hamiltonian is only semi-convex. A variational principle is also used to establish existence for the corresponding Cauchy...

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we study the geometry of a semi-Riemannian manifold ¯ M of quasi-constant curvature. The main result is two characterization theorems for ¯ M admits solenoidal and screen totally umbilical r (> 1)-lightlike subm...

In this paper, we obtain some classification theorems for totally umbilical semi-invariant submanifolds in locally decomposable metallic Riemannian manifolds. We also prove that there exist no proper a posivitely or negatively curved manifold

Let (M, g) be a compact Riemannian manifold of dimension n ≥ 3 with boundary ∂M . We denote the Ricci curvature, scalar curvature, mean curvature, and the second fundamental form by Ric, R , h, and Lαβ , respectively. The Yamabe problem for manifolds with boundary is to find a conformal metric ĝ = eg such that the scalar curvature is constant and the mean curvature is zero. The boundary is call...