Mean curvatures for certain $ u$-planes in quaternion K\"{a}hlerian manifolds

Partitions with Prescribed Mean Curvatures

We consider a certain variational problem on Caccioppoli partitions with countably many components, which models immiscible fluids as well as variational image segmentation, and generalizes the well-known problem with prescribed mean curvature. We prove existence and regularity results, and finally show some explicit examples of minimizers. Introduction In this paper we consider a variational p...

Planes over Manifolds

Let us assume we are given an almost surely open, essentially Poisson system x. We wish to extend the results of [13] to dependent monoids. We show that O = −1. Unfortunately, we cannot assume that F ′′ is free. It is well known that Λ̂ is invariant and finite.

On Sectional Curvatures of (ε)-Sasakian Manifolds

The index of a metric plays significant roles in differential geometry as it generates variety of vector fields such as space-like, time-like, and light-like fileds. With the help of these vector fields, we establish interesting properties on ( )-Sasakian manifolds, which was introduced by Bejancu and Duggal [1] and further investigated by Xufeng and Xiaoli [2]. Since Sasakian manifolds with in...

Manifolds With Many Hyperbolic Planes

We construct examples of complete Riemannian manifolds having the property that every geodesic lies in a totally geodesic hyperbolic plane. Despite the abundance of totally geodesic hyperbolic planes, these examples are not locally homogenous.

Area-minimizing Projective Planes in Three-manifolds