The density of integral points on hypersurfaces of degree at least four
Oscar Marmon (2010)
Acta Arithmetica
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Oscar Marmon (2010)
Acta Arithmetica
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Kim, Hyang Sook, Pyo, Yong-Soo (1998)
Balkan Journal of Geometry and its Applications (BJGA)
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Grzegorz Łubczonok (1981)
Colloquium Mathematicae
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F. Constantinescu, J. G. Taylor (1973)
Recherche Coopérative sur Programme n°25
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Enrico Bombieri, Julia Mueller, Umberto Zannier (2001)
Acta Arithmetica
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M. D. Prešić (1970)
Matematički Vesnik
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Gaál, István, Pethö, Attila, Pohst, Michael (1994)
Experimental Mathematics
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Takehiro Itoh, Sadahiro Maeda (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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We characterize totally η-umbilic real hypersurfaces in a nonflat complex space form M̃ₙ(c) (= ℂPⁿ(c) or ℂHⁿ(c)) and a real hypersurface of type (A₂) of radius π/(2√c) in ℂPⁿ(c) by observing the shape of some geodesics on those real hypersurfaces as curves in the ambient manifolds (Theorems 1 and 2).
Shabbir, Ghulam, Amur, Khuda Bux (2006)
APPS. Applied Sciences
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Jeffrey Stuart (2016)
Czechoslovak Mathematical Journal
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W. J. Ellison (1970-1971)
Séminaire de théorie des nombres de Bordeaux
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Arne Winterhof (2001)
Acta Arithmetica
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Christophe Mourougane (2012)
Journal of the European Mathematical Society
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Grauert and Manin showed that a non-isotrivial family of compact complex hyperbolic curves has finitely many sections. We consider a generic moving enough family of high enough degree hypersurfaces in a complex projective space. We show the existence of a strict closed subset of its total space that contains the image of all its sections.
Barbara Opozda, Udo Simon (2014)
Annales Polonici Mathematici
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We investigate parallel hypersurfaces in the context of relative hypersurface geometry, in particular including the cases of Euclidean and Blaschke hypersurfaces. We describe the geometric relations between parallel hypersurfaces in terms of deformation operators, and we apply the results to the parallel deformation of special classes of hypersurfaces, e.g. quadrics and Weingarten hypersurfaces.
Juan de Dios Pérez, Young Jin Suh, Changhwa Woo (2015)
Open Mathematics
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In this paper we prove a non-existence of real hypersurfaces in complex hyperbolic two-plane Grassmannians SU2.m/S(U2·Um), m≥3, whose structure tensors {ɸi}i=1,2,3 commute with the shape operator.
Cícero P. Aquino, Henrique F. de Lima, Fábio R. dos Santos, Marco Antonio L. Velásquez (2015)
Commentationes Mathematicae Universitatis Carolinae
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Our aim is to apply suitable generalized maximum principles in order to obtain characterization results concerning complete linear Weingarten hypersurfaces immersed in a locally symmetric Riemannian manifold, whose sectional curvature is supposed to obey standard constraints. In this setting, we establish sufficient conditions to guarantee that such a hypersurface must be either totally umbilical or an isoparametric hypersurface with two distinct principal curvatures one of which is...
H. Grosse (1987)
Recherche Coopérative sur Programme n°25
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Young Ho Kim, Sadahiro Maeda (2011)
Colloquium Mathematicae
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We characterize homogeneous real hypersurfaces of types (A₀), (A₁) and (B) in a complex projective space or a complex hyperbolic space.
Yu-Ru Liu, Craig V. Spencer, Xiaomei Zhao (2010)
Acta Arithmetica
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