Note on two three-dimensional manifolds with the same group

On three dimensional stellar manifolds

It is well known that a three dimensional (closed, connected and compact) manifold is obtained by identifying boundary faces from a stellar ball a ⋆ S. The study of S/ ∼, two dimensional stellar sphere S with 2-simplexes identified in pairs leads us to the following conclusion: either a three dimensional manifold is homeomorphic to a sphere or to a stellar ball a⋆S with its boundary 2-simplexes...

On three-dimensional $N(k)$-paracontact metric manifolds and Ricci solitons

The aim of this paper is to characterize $3$-dimensional $N(k)$-paracontact metric manifolds satisfying certain curvature conditions. We prove that a $3$-dimensional $N(k)$-paracontact metric manifold $M$ admits a Ricci soliton whose potential vector field is the Reeb vector field $xi$ if and only if the manifold is a paraSasaki-Einstein manifold. Several consequences of this result are discuss...

On Three-dimensional Cauchy-riemann Manifolds

of the almost complex tensor of C2 ("multiplication by i "). The collection of these subspaces HpM forms a bundle H MeT M called the horizontal or contact bundle. (Indeed, strict pseudoconvexity of M implies that the plane field {HpM} is nondegenerate, i.e. defines a contact structure.) The almost complex tensor of C2 then restricts to a bundle endomorphism J : H M -+ H M such that J2 = -id. Th...

Two and Three-Dimensional Seepage Analysis of Earth Dams Considering Horizontal Filter Blanket Effects (RESEARCH NOTE)

Prescribing Curvatures on Three Dimensional Riemannian Manifolds with Boundaries

Let (M, g) be a complete three dimensional Riemannian manifold with boundary ∂M . Given smooth functions K(x) > 0 and c(x) defined on M and ∂M , respectively, it is natural to ask whether there exist metrics conformal to g so that under these new metrics, K is the scalar curvature and c is the boundary mean curvature. All such metrics can be described by a prescribing curvature equation with a ...