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On some properties of induced almost contact structures

Zuzanna Szancer (2015)

Annales Polonici Mathematici

Real affine hypersurfaces of the complex space n + 1 with a J-tangent transversal vector field and an induced almost contact structure (φ,ξ,η) are studied. Some properties of the induced almost contact structures are proved. In particular, we prove some properties of the induced structure when the distribution is involutive. Some constraints on a shape operator when the induced almost contact structure is either normal or ξ-invariant are also given.

On superminimal surfaces

Thomas Friedrich (1997)

Archivum Mathematicum

Using the Cartan method O. Boruvka (see [B1], [B2]) studied superminimal surfaces in four-dimensional space forms. In particular, he described locally the family of all superminimal surfaces and classified all of them with a constant radius of the indicatrix. We discuss the mentioned results from the point of view of the twistor theory, providing some new proofs. It turns out that the superminimal surfaces investigated by geometers at the beginning of this century as well as by O. Boruvka...

On tensor functions whose gradients have some skew-symmetries

Adriano Montanaro (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let V n be a real inner product space of any dimension; and let Q α 1 α v = Q α 1 α v X β 1 β τ be a C 2 -map relating any two tensor spaces on V n . We study the consequences imposed on the form of this function by the condition that its gradient should be skew-symmetric with respect to some pairs α μ , β η of indexes. Any such a condition is written as a system of linear partial differential equations, with constant coefficients, which is symmetric with respect to certain couples of independent variables. The solutions of these systems appear...

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