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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 ℝ 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 ( ℝ 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.

Minimal surfaces in pseudohermitian geometry

Jih-Hsin Cheng, Jenn-Fang Hwang, Andrea Malchiodi, Paul Yang (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group. We interpret the p-mean curvature not only as the tangential sublaplacian of a defining function, but also as the curvature of a characteristic curve, and as a quantity in terms of calibration geometry. As a differential equation, the p-minimal surface equation...

Minimal surfaces in sub-riemannian manifolds and structure of their singular sets in the ( 2 , 3 ) case

Nataliya Shcherbakova (2009)

ESAIM: Control, Optimisation and Calculus of Variations

We study minimal surfaces in sub-riemannian manifolds with sub-riemannian structures of co-rank one. These surfaces can be defined as the critical points of the so-called horizontal area functional associated with the canonical horizontal area form. We derive the intrinsic equation in the general case and then consider in greater detail 2 -dimensional surfaces in contact manifolds of dimension 3 . We show that in this case minimal surfaces are projections of a special class of 2 -dimensional surfaces...

Minimal surfaces in sub-Riemannian manifolds and structure of their singular sets in the (2,3) case

Nataliya Shcherbakova (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We study minimal surfaces in sub-Riemannian manifolds with sub-Riemannian structures of co-rank one. These surfaces can be defined as the critical points of the so-called horizontal area functional associated with the canonical horizontal area form. We derive the intrinsic equation in the general case and then consider in greater detail 2-dimensional surfaces in contact manifolds of dimension 3. We show that in this case minimal surfaces are projections of a special class of 2-dimensional surfaces...

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