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The integrability of a field of endomorphisms

Gerard Thompson (2002)

Mathematica Bohemica

A Theorem is proved that gives intrinsic necessary and sufficient conditions for the integrability of a zero-deformable field of endomorphisms. The Theorem is proved by reducing to a special case in which the endomorphism field is nilpotent. Many arguments used in the derivation of similar results are simplified, principally by means of using quotient rather than subspace constructions.

Weighted minimal translation surfaces in the Galilean space with density

Dae Won Yoon (2017)

Open Mathematics

Translation surfaces in the Galilean 3-space G3 have two types according to the isotropic and non-isotropic plane curves. In this paper, we study a translation surface in G3 with a log-linear density and classify such a surface with vanishing weighted mean curvature.

Weingarten hypersurfaces of the spherical type in Euclidean spaces

Cid D. F. Machado, Carlos M. C. Riveros (2020)

Commentationes Mathematicae Universitatis Carolinae

We generalize a parametrization obtained by A. V. Corro in (2006) in the three-dimensional Euclidean space. Using this parametrization we study a class of oriented hypersurfaces M n , n ≥ 2 , in Euclidean space satisfying a relation ∑ r = 1 n ( - 1 ) r + 1 r f r - 1 n r H r = 0 , where H r is the r th mean curvature and f ∈ C ∞ ( M n ; ℝ ) , these hypersurfaces are called Weingarten hypersurfaces of the spherical type. This class of hypersurfaces includes the surfaces of the spherical type (Laguerré minimal surfaces). We characterize these hypersurfaces in terms of harmonic...

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