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Minimal Graphs in n × and n + 1

Ricardo Sà Earp, Eric Toubiana (2010)

Annales de l’institut Fourier

We construct geometric barriers for minimal graphs in n × . We prove the existence and uniqueness of a solution of the vertical minimal equation in the interior of a convex polyhedron in n 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 n × , we solve the Dirichlet problem for the vertical minimal equation in a C 0 convex domain Ω n taking arbitrarily continuous finite boundary and asymptotic boundary data.We prove...

Minimal Reeb vector fields on almost Kenmotsu manifolds

Yaning Wang (2017)

Czechoslovak Mathematical Journal

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 ( k , μ , ν ) -almost Kenmotsu manifolds. Also, we give some characterizations of the minimality of the Reeb vector fields of ( k , μ , ν ) -almost Kenmotsu manifolds. In addition, we prove that the Reeb vector field of an almost Kenmotsu manifold with conformal Reeb foliation is minimal.

Minimal slant submanifolds of the smallest dimension in S-manifolds.

Alfonso Carriazo, Luis M. Fernández, María Belén Hans-Uber (2005)

Revista Matemática Iberoamericana

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.

Minimal submanifolds in 4 with a g.c.K. structure

Marian-Ioan Munteanu (2008)

Czechoslovak Mathematical Journal

In this paper we obtain all invariant, anti-invariant and C R submanifolds in ( 4 , g , J ) 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.

Minimal submanifolds in general (α,β)-spaces

Songting Yin, Qun He, Dinghe Xie (2013)

Annales Polonici Mathematici

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.

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