2016
DOI: 10.1016/j.difgeo.2016.10.002
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Constant mean curvature hypersurfaces with constant angle in semi-Riemannian space forms

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Cited by 9 publications
(6 citation statements)
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“…We should notice that submanifolds with constant function correspond to a natural extension of hypersurfaces with constant angle in a product space, which was widely studied by Dillen and many other authors (see, for instance [12, 13, 23, 24]).…”
Section: Resultsmentioning
confidence: 99%
“…We should notice that submanifolds with constant function correspond to a natural extension of hypersurfaces with constant angle in a product space, which was widely studied by Dillen and many other authors (see, for instance [12, 13, 23, 24]).…”
Section: Resultsmentioning
confidence: 99%
“…In the case of semi-Riemannian spaceforms, when viewed as hyperquadrics immersed in a semi-Euclidean space, CC vector fields arise as projections of parallel vector fields defined on the respective semi-Euclidean space [34,21]. Notice that according to Eq.…”
Section: Closed Conformal Vector Fieldsmentioning
confidence: 99%
“…Recall that in the semi-Riemannian setting, constant angle hypersurfaces can be defined via the squared norm of V /|V |, or equivalently, the squared norm of V ⊥ /|V |; where V and V ⊥ denote the tangent and normal components of V . Thus Lemma 4.2 can be interpreted as a generalization to the null context of this classical result (see for instance Lemma 3.3 in [34]).…”
mentioning
confidence: 94%
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“…Furthermore, any Riemannian manifold possessing a non-trivial closed and conformal vector field is locally a warped product with base a real interval, and the complete ones are either the Euclidean space or the sphere with a rotationally invariant metric or a quotient of a warped product (see [12]). The presence of a closed conformal vector field in the ambient space is a very helpful property that has been considered in several works to establish classification results in recent years (see, for instance, [5,6,8,11,13]).…”
Section: Má Meroño Mjommentioning
confidence: 99%