ON $\mathcal{T}$-HYPERSURFACES OF A PARASASAKIAN MANIFOLD

On hypersurfaces in a locally affine Riemannian Banach manifold II

In our previous work (2002), we proved that an essential second-order hypersurface in an infinite-dimensional locally affine Riemannian Banach manifold is a Riemannian manifold of constant nonzero curvature. In this note, we prove the converse; in other words, we prove that a hypersurface of constant nonzero Riemannian curvature in a locally affine (flat) semiRiemannian Banach space is an essen...

Hypersurfaces in a quasi Kähler manifold

Okumura gave a necessary and sufficient condition for an oriented real hypersurface of a Kähler manifold to be a contact metric manifold with respect to the naturally induced almost contact metric structure. In this paper, we discuss an oriented hypersurface of a quasi Kähler manifold and give a necessary and sufficient condition for such a hypersurface to be a quasi contact metric manifold wit...

On Hypersurfaces in a Locally Affine Riemannian Banach Manifold

On the Manifold of Closed Hypersurfaces in R

Several results from differential geometry of hypersurfaces in Rn are derived to form a tool box for the direct mapping method. The latter technique has been widely employed to solve problems with moving interfaces, and to study the asymptotics of the induced semiflows.

Examples of hypersurfaces flowing by curvature in a Riemannian manifold

This paper gives some examples of hypersurfaces φt(M ) evolving in time with speed determined by functions of the normal curvatures in an (n+ 1)-dimensional hyperbolic manifold; we emphasize the case of flow by harmonic mean curvature. The examples converge to a totally geodesic submanifold of any dimension from 1 to n, and include cases which exist for infinite time. Convergence to a point was...