RIBAUCOUR TRANSFORMATIONS ON RIEMANNIAN SPACE FORMS IN LORENTZIAN SPACE FORM

In this paper, we show that biharmonic hypersurfaces with at most two distinct principal curvatures in pseudo-Riemannian space form Nsn+1c with constant sectional curvature c and index s have constant mean curvature. Furthermore, we find that such biharmonic hypersurfaces Mr2k−1 in even-dimensional pseudo-Euclidean space Es2k, Ms−12k−1 in even-dimensional de Sitter space Ss2kcc>0, and Ms2k−1 in even-dimensional anti-de Sitter space ℍs2kcc<0 are minimal.

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Biharmonic hypersurfaces in pseudo-Riemannian space forms

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887816500948 ◽

2016 ◽

Vol 13 (07) ◽

pp. 1650094 ◽

Cited By ~ 1

Author(s):

Dan Yang ◽

Yu Fu

Keyword(s):

Sectional Curvature ◽

Mean Curvature ◽

Riemannian Space ◽

Constant Mean Curvature ◽

Space Form ◽

Constant Sectional Curvature ◽

Principal Curvatures ◽

Space Forms ◽

Riemannian Space Forms

Let [Formula: see text] be a nondegenerate biharmonic pseudo-Riemannian hypersurface in a pseudo-Riemannian space form [Formula: see text] with constant sectional curvature [Formula: see text]. We show that [Formula: see text] has constant mean curvature provided that it has three distinct principal curvatures and the Weingarten operator can be diagonalizable.

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On biconservative hypersurfaces in pseudo-Riemannian space forms and their Gauss map

Publications de l Institut Mathematique ◽

10.2298/pim1817223t ◽

2018 ◽

Vol 103 (117) ◽

pp. 223-236 ◽

Cited By ~ 1

Author(s):

Nurettin Turgay

Keyword(s):

Euclidean Space ◽

Minkowski Space ◽

Mean Curvature ◽

Riemannian Space ◽

Space Form ◽

Gauss Map ◽

Space Forms ◽

Geometrical Properties ◽

Riemannian Space Forms ◽

Biconservative Hypersurfaces

We first present a survey about recent results on biconservative hypersurfaces in the Minkowski space E4 1, pseudo-Euclidean space E5 2 and Rieamnnian space-form H4. Then we obtain some geometrical properties of these hypersurface families concerning their mean curvature and Gauss map.

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2-symmetric lightlike hypersurfaces in semi-Riemannian space forms

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887814500893 ◽

2014 ◽

Vol 11 (10) ◽

pp. 1450089

Author(s):

Süleyman Cengiz ◽

Ali Görgülü

Keyword(s):

Riemannian Space ◽

Space Form ◽

Symmetry Type ◽

Space Forms ◽

Lightlike Hypersurface ◽

Riemannian Space Forms ◽

Lightlike Hypersurfaces

In this paper, we will investigate 2-symmetry type curvature conditions of a lightlike hypersurface of a semi-Riemannian space form. Then we find some results related with locally symmetric and 2-symmetric lightlike hypersurfaces. Finally the relation between semisymmetric and 2-symmetric lightlike hypersurfaces will be given.

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Uniqueness of Curvature Measures in Pseudo-Riemannian Geometry

Journal of Geometric Analysis ◽

10.1007/s12220-021-00702-4 ◽

2021 ◽

Author(s):

Andreas Bernig ◽

Dmitry Faifman ◽

Gil Solanes

Keyword(s):

Riemannian Manifolds ◽

Riemannian Geometry ◽

Riemannian Space ◽

Space Forms ◽

Type Formula ◽

Isometric Embeddings ◽

Curvature Measures ◽

Riemannian Space Forms

AbstractThe recently introduced Lipschitz–Killing curvature measures on pseudo-Riemannian manifolds satisfy a Weyl principle, i.e. are invariant under isometric embeddings. We show that they are uniquely characterized by this property. We apply this characterization to prove a Künneth-type formula for Lipschitz–Killing curvature measures, and to classify the invariant generalized valuations and curvature measures on all isotropic pseudo-Riemannian space forms.

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