18,077 research outputs found
On submanifolds whose shape operator is unipotent
No full textThe object of this article is to characterize submanifolds of the Euclidean space whose shape operator is unipoten
Minimal Immersions of Kahler manifolds into Euclidean Spaces
No full textIt is proved here that a minimal isometric immersion of a Kähler-Einstein or homogeneous Kähler-manifold into an Euclidean space must be totally geodesic
Autoparallel distributions and splitting theorems
No full textWe study some links between autoparallel distributions and the factorization of a riemannian manifold. Finally, we prove a splitting theorem for Lie groups with biinvariant metric
Codimension reduction in symmetric spaces
No full textIn this paper we give a short geometric proof of a generalization of a well-known result about reduction of codimension for submanifolds of Riemannian symmetric spacesFil: Di Scala, Antonio. Politecnico di Torino; ItaliaFil: Vittone, Francisco. Universidad Nacional de Rosario. Facultad de Cs.exactas Ingeniería y Agrimensura. Escuela de Cs.exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
Weak helix submanifolds of euclidean spaces
No full textIt is shown that there exist nonstrong weak 2-helix surfaces of R
Minimal homogeneous submanifolds in euclidean spaces
No full textWe prove that minimal (extrinsically) homogeneous submanifolds of the Euclidean space are totally geodesic. As an application, we obtain that a complex (intrisecally) homogeneous submanifold of a complex Euclidean space must be totally geodesic
Mok's characteristic varieties and the normal holonomy group
No full textIn this paper we complete the study of the normal holonomy groups of complex submanifolds (non nec. complete) of Cn or CPn. We show that irreducible but non-transitive normal holonomies are exactly the Hermitian s-representations of [4, Table 1] (see Corollary 1.1). For each one of them we construct a non necessarily complete complex submanifold whose normal holonomy is the prescribed s-representation. We also show that if the submanifold has irreducible non-transitive normal holonomy then it is an open subset of the smooth part of one of the characteristic varieties studied by N. Mok in his work about rigidity of locally symmetric spaces. Finally, we prove that if the action of the normal holonomy group of a projective submanifold is reducible then the submanifold is an open subset of the smooth part of a so called join, i.e. the union of the lines joining two projective submanifolds.Fil: Di Scala, Antonio J.. Politecnico di Torino; ItaliaFil: Vittone, Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentin
Connected subgroups of SO(2,n) acting irreducibly on R^{2,n}
No full textWe classify all connected subgroups of SO(2, n) that act irreducibly on R^{2, n
Geometry applications of irreducible representations of Lie Groups
No full textIn this note we give proofs of the following three algebraic facts which have applications in the theory of holonomy groups and homogeneous spaces: Any irreducibly acting connected subgroup G \subset Gl(n,\rr) is closed. Moreover, if admits an invariant bilinear form of Lorentzian signature, is maximal, i.e. it is conjugated to . We calculate the vector space of -invariant symmetric bilinear forms, show that it is at most -dimensional, and determine the maximal stabilizers for each dimension. Finally, we give some applications and present some open problem
Reducibility of complex submanifolds of the complex euclidean spaces
No full textLet M be a simply connected complex submanifold of CN. We prove that M is irreducible, up a totally geodesic factor,if and only if the normal holonomy group acts irreducibly. This is an extrinsic analogue of the well-known De Rham decomposition theorem for a complex manifold. Our result is not valid in the real context, as it is shown by many counterexamples
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