Cauchy-Kowalewski extension theorems and representations of analytic functionals acting over special classes of real n-dimensional submanifolds of
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Ryan, John (1984)
Proceedings of the 11th Winter School on Abstract Analysis
Ryszard Deszcz, Miroslava Petrović-Torgašev, Zerrin Şentürk, Leopold Verstraelen (2010)
Publications de l'Institut Mathématique
Toshiaki Adachi, Sadahiro Maeda (2005)
Czechoslovak Mathematical Journal
In this paper we characterize totally umbilic hypersurfaces in a space form by a property of the extrinsic shape of circles on hypersurfaces. This characterization corresponds to characterizations of isoparametric hypersurfaces in a space form by properties of the extrinsic shape of geodesics due to Kimura-Maeda.
Johan Deprez, Piet A. Verheyen, Leopold C. A. Verstraelen (1985)
Czechoslovak Mathematical Journal
N. Abe, Y. Nakanishi, S. Yamagushi (1990)
Aequationes mathematicae
Shin-Ichi Kawamoto (1994)
Revista Matemática de la Universidad Complutense de Madrid
We study real submanifolds of a complex hyperbolic space and prove a codimension reduction theorem.
Matsuyama, Yoshio (2009)
Balkan Journal of Geometry and its Applications (BJGA)
Mehmet Bektaş, Mahmut Ergüt (1999)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
Kim, Hyang Sook, Pyo, Yong-Soo (1999)
Balkan Journal of Geometry and its Applications (BJGA)
Jens Chr. Larsen (1996)
Monatshefte für Mathematik
Ianus, S., Matsumoto, K., Ornea, L. (1987)
Publications de l'Institut Mathématique. Nouvelle Série
Gérard A. Maugin (1976)
Annales de l'I.H.P. Physique théorique
Jovanka Nikić (2003)
Kragujevac Journal of Mathematics
Dorić, M., Petrović-Torgašev, M., Verstraelen, L. (1988)
Publications de l'Institut Mathématique. Nouvelle Série
Marco Rigoli, Isabel M.C. Salavessa (1987)
Mathematische Zeitschrift
Vladimir Rovenski (2005)
Annales Polonici Mathematici
We introduce and study submanifolds with extrinsic curvature and second fundamental form related by an inequality that holds for isotropic submanifolds and becomes equality for totally umbilical submanifolds. The dimension of umbilical subspaces and the index of conformal nullity of these submanifolds with low codimension are estimated from below. The corollaries are characterizations of extrinsic spheres in Riemannian spaces of positive curvature.
Jean-Marie Morvan, Georges Zafindratafa (1986/1987)
Annales de la Faculté des sciences de Toulouse : Mathématiques
Chen, Bang-Yen, Garay, Oscar J. (2003)
International Journal of Mathematics and Mathematical Sciences
Alexandre A. M. Rodrigues (2007)
Banach Center Publications
Goldberg, Vladislav V., Rosca, Radu (1984)
International Journal of Mathematics and Mathematical Sciences
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