Minimal deformation of a non-full minimal surface in
We construct geometric barriers for minimal graphs in We prove the existence and uniqueness of a solution of the vertical minimal equation in the interior of a convex polyhedron in extending continuously to the interior of each face, taking infinite boundary data on one face and zero boundary value data on the other faces.In , we solve the Dirichlet problem for the vertical minimal equation in a convex domain taking arbitrarily continuous finite boundary and asymptotic boundary data.We prove...
A necessary and sufficient condition for the Reeb vector field of a three dimensional non-Kenmotsu almost Kenmotsu manifold to be minimal is obtained. Using this result, we obtain some classifications of some types of -almost Kenmotsu manifolds. Also, we give some characterizations of the minimality of the Reeb vector fields of -almost Kenmotsu manifolds. In addition, we prove that the Reeb vector field of an almost Kenmotsu manifold with conformal Reeb foliation is minimal.
We study slant submanifolds of S-manifolds with the smallest dimension, specially minimal submanifolds and establish some relations between them and anti-invariant submanifolds in S-manifolds, similar to those ones proved by B.-Y. Chen for slant surfaces and totally real surfaces in Kaehler manifolds.
In this paper we obtain all invariant, anti-invariant and submanifolds in endowed with a globally conformal Kähler structure which are minimal and tangent or normal to the Lee vector field of the g.c.K. structure.
The volume forms of general (α,β)-metrics are studied. Some equations for minimal submanifolds in general (α,β)-spaces are established by using the normal frame field, and some minimal surfaces in general (α,β)-spaces with special curvature properties are constructed.