Parabolic submanifolds of rank two

Dajczer, Marcos; Morais, Pedro

doi:10.21711/231766362008/rmc349

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Corollary 2 Under the Assumptions Of Theorem 1 Cases1

Introduction1

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2014

2015

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Cited by 2 publications

(2 citation statements)

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“…The submanifolds in case (i) have been studied in [2] and [3], where a parametric classification has been obtained in most cases.…”

Section: Corollary 2 Under the Assumptions Of Theorem 1 Casesmentioning

confidence: 99%

Submanifolds with nonparallel first normal bundle revisited

Dajczer¹,

Tojeiro²

2014

Publicacions Matemàtiques

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“…The submanifolds in case (i) have been studied in [2] and [3], where a parametric classification has been obtained in most cases.…”

Section: Corollary 2 Under the Assumptions Of Theorem 1 Casesmentioning

confidence: 99%

Submanifolds with nonparallel first normal bundle revisited

Dajczer¹,

Tojeiro²

2014

Publicacions Matemàtiques

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“…Euclidean submanifolds of rank two have been studied in different contexts; see [1], [7], [8], [11] and [12]. A submanifold having rank two means that the image of the Gauss map is a surface in the corresponding Grassmannian or, equivalently, that the kernel of the second fundamental form (relative nullity subspace) has constant codimension two.…”

Section: Introductionmentioning

confidence: 99%

The associated family of an elliptic surface and an application to minimal submanifolds

Dajczer

Vlachos

2015

Geom Dedicata

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It is well-known that in any codimension a simply connected Euclidean minimal surface has an associated one-parameter family of minimal isometric deformations. In this paper, we show that this is just a special case of the associated family to any simply connected elliptic surface for which all curvature ellipses of a certain order are circles. We also provide the conditions under which this associated family is trivial, extending the known result for minimal surfaces. As an application, we show how the associated family of a minimal Euclidean submanifold of rank two is determined by the associated family of an elliptic surface clarifying the geometry around the associated family of these higher dimensional submanifolds.

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Parabolic submanifolds of rank two

Cited by 2 publications

References 8 publications

Submanifolds with nonparallel first normal bundle revisited

Submanifolds with nonparallel first normal bundle revisited

The associated family of an elliptic surface and an application to minimal submanifolds

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