Zobrazeno 1 - 10
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pro vyhledávání: '"Renato Tribuzy"'
We give necessary and sufficient conditions on a smooth local map of a Riemannian manifold $M^m$ into the sphere $S^m$ to be the Gauss map of an isometric immersion $u:M^m \to R^n$, $n=m+1$. We briefly discuss the case of general $n$ as well
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Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::61b8b33b47a0e4649e14870220204e2e
https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/38976
https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/38976
A submanifold M ⊂ R n lies in the sphere S n − 1 iff it carries a parallel umbilic normal vector field. We extend this theorem by replacing the sphere S n − 1 by an arbitrary extrinsic symmetric space S ⊂ R n .
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bd1b4859fe7f7b16f1858ce6d0c11998
https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/38963
https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/38963
Autor:
Maria João Ferreira, Renato Tribuzy
Publikováno v:
Ark. Mat. 52, no. 1 (2014), 93-98
We present a reduction of codimension theorem for surfaces with parallel mean curvature in symmetric spaces.
Publikováno v:
Transactions of the American Mathematical Society. 364:6229-6258
Autor:
Renato Tribuzy, Harold Rosenberg
Publikováno v:
Bulletin des Sciences Mathématiques. 136(8):892-898
We prove rigidity of oriented isometric immersions of complete surfaces in the homogeneous 3-manifolds E ( k , τ ) (different from the space forms) having the same positive extrinsic curvature, and satisfying a one-point condition.
Publikováno v:
Annali di Matematica Pura ed Applicata. 193:517-527
We assume that an immersed constant mean curvature surface $${\varSigma } \looparrowright {M_k} \times \mathbb R $$ satisfies a relation involving the mean curvature, the Gaussian curvature and the angle that the unit vector of the factor $$\mathbb R
Publikováno v:
Differential Geometry and its Applications. 27:691-695
Immersions with parallel pluri-mean curvature into euclidean n-space generalize constant mean curvature immersions of surfaces to Kahler manifolds of complex dimension m. Examples are the standard embeddings of Kahler symmetric spaces into the Lie al
Publikováno v:
Communications in Analysis and Geometry. 15:283-298
Publikováno v:
Differential Geometry and its Applications. 20(1):47-66
We investigate the local geometry of a class of K\"ahler submanifolds $M \subset \R^n$ which generalize surfaces of constant mean curvature. The role of the mean curvature vector is played by the $(1,1)$-part (i.e. the $dz_id\bar z_j$-components) of
Publikováno v:
Qualitative Theory of Dynamical Systems. 2:207-220
We establish the differential equation of the lines of curvature for immersions of surfaces into ℝ4. From the point of view of principal lines of curvature, we show that the differnetila equations under consideration carry almost complete informati